List of Publications:

  1. On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators. Doc. Math. 8 (2003), 547 - 565. Article
  2. (with R.G. Shterenberg) On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering. Doc. Math. 9 (2004), 57 - 77. Article
  3. On the Laplacian in the halfspace with a periodic boundary condition. Ark. Mat. 44 (2006), no. 2, 277 - 298. Article - Preprint
  4. On the tunneling effect for magnetic Schrödinger operators in antidot lattices. Asymptot. Anal. 48 (2006), no. 1-2, 91 - 120. Article - Preprint
  5. (with R.G. Shterenberg) On the spectrum of partially periodic operators. In: Operator Theory, Analysis and Mathematical Physics, J. Janas, et al. (eds.), 35 - 50, Oper. Theory Adv. Appl. 174, Birkhäuser, Basel, 2007. Article - Preprint
  6. (with O. Safronov) Absolutely continuous spectrum of a class of random nonergodic Schrödinger operators. Int. Math. Res. Not. (2005), no. 42, 2559 - 2577. Article - Preprint
  7. (with P. Exner) Absolute continuity of the spectrum for periodically modulated leaky wires in R3. Ann. Henri Poincaré 8 (2007), no. 2, 241 - 263. Article - Preprint
  8. (with T. Ekholm) On Lieb-Thirring inequalities for Schrödinger operators with virtual level. Comm. Math. Phys. 264 (2006), no. 3, 725 - 740. Article - Preprint
  9. On the asymptotic number of edge states for magnetic Schrödinger operators. Proc. London Math. Soc. (3) 95 (2007), no. 1, 1 - 19. Article - Preprint
  10. (with A. Laptev, E.H. Lieb and R. Seiringer) Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Lett. Math. Phys. 77 (2006), 309 - 316. Article - Preprint
  11. (with E.H. Lieb and R. Seiringer) Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators. J. Amer. Math. Soc. 21 (2008), no. 4, 925 - 950. Article - Preprint
  12. (with E.H. Lieb and R. Seiringer) Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value. Comm. Math. Phys. 275 (2007), no. 2, 479 - 489. Article - Preprint
  13. (with T. Ekholm) Lieb-Thirring inequalities on the half-line with critical exponent. J. Eur. Math. Soc. 10 (2008), no. 3, 739 - 755. Article - Preprint
  14. (with A.M. Hansson) Eigenvalue estimates for the Aharonov-Bohm operator in a domain. In: Methods of Spectral Analysis in Mathematical Physics, J. Janas, et al. (eds.), 35 - 50, Oper. Theory Adv. Appl. 186, Birkhäuser, Basel, 2008. Article - Preprint
  15. (with H. Siedentop and S. Warzel) The ground state energy of heavy atoms: relativistic lowering of the leading energy correction. Comm. Math. Phys. 278 (2008), no. 2, 549 - 566. Article - Preprint
  16. (with C. Hainzl, S. Naboko and R. Seiringer) The critical temperature in the BCS model at weak coupling. J. Geom. Anal. 17 (2007), no. 4, 559 - 568. Article - Preprint
  17. (with R.D. Benguria and M. Loss) The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space. Math. Res. Lett. 15 (2008), no. 4, 613 - 622. Article - Preprint
  18. (with E.H. Lieb, R. Seiringer and H. Siedentop) Müller's exchange-correlation energy in density-matrix-functional theory. Phys. Rev. A 76 (2007), 052517. Article - Preprint
  19. (with A. Laptev and S. Molchanov) Eigenvalue estimates for magnetic Schrödinger operators in domains. Proc. Amer. Math. Soc. 136 (2008), no. 12, 4245 - 4255. Article - Preprint
  20. (with B. Simon and T. Weidl) Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states. Comm. Math. Phys. 282 (2008), no. 1, 199 - 208. Article - Preprint
  21. (with M. Loss and T. Weidl) Polya's conjecture in the presence of a constant magnetic field. J. Eur. Math. Soc. 11 (2009), 1365 - 1383. Article - Preprint
  22. (with E.H. Lieb and R. Seiringer) Number of bound states of Schrödinger operators with matrix-valued potentials. Lett. Math. Phys. 82 (2007), 107 - 116. Article - Preprint
  23. (with T. Ekholm and H. Kovarik) Eigenvalue estimates for Schrödinger operators on metric trees. Adv. Math. 226 (2011), 5165 - 5197. Article - Preprint
  24. (with T. Ekholm and H. Kovarik) Remarks about Hardy inequalities on metric trees. In: Analysis on graphs and its applications, P. Exner, et al. (eds.), 369 - 379, Proc. Sympos. Pure Math. 77, Amer. Math. Soc., Providence, RI, 2008. Article - Preprint
  25. (with A. Laptev) Spectral inequalities for Schrödinger operators with surface potentials. In: Spectral theory of differential operators, T. Suslina and D. Yafaev (eds.), 91 - 102, Amer. Math. Soc. Transl. Ser. 2, 225 (2008). Article - Preprint
  26. (with R. Seiringer) Non-linear ground state representations and sharp Hardy inequalities. J. Funct. Anal. 255 (2008), 3407 - 3430. Article - Preprint
  27. (with H. Siedentop and S. Warzel) The energy of heavy atoms according to Brown and Ravenhall: the Scott correction. Doc. Math. 14 (2009), 463 - 516. Article - Preprint
  28. (with J. Breuer) Singular spectrum for radial trees. Rev. Math. Phys. 21 (2009), no. 7, 1 - 17. Article - Preprint
  29. A simple proof of Hardy-Lieb-Thirring inequalities. Comm. Math. Phys. 290 (2009), no. 2, 789 - 800. Article - Preprint
  30. A note on low energy scattering for homogeneous long-range potentials. Ann. Henri Poincaré 10 (2009), no. 3, 573 - 575. Article - Preprint
  31. Remarks on eigenvalue estimates and semigroup domination. In: Spectral and Scattering Theory for Quantum Magnetic Systems, P. Briet, et al. (eds.), 63 - 86, Contemp. Math. 500, Amer. Math. Soc., Providence, RI, 2009. Article - Preprint
  32. (with A. Laptev and R. Seiringer) A sharp bound on eigenvalues of Schrödinger operators on the halfline with complex-valued potentials. In: Spectral Theory and Analysis, J. Janas et al. (eds.), 39 - 44, Oper. Theory Adv. Appl. 214, Birkhäuser, Basel, 2011. Article - Preprint
  33. (with S. Morozov and S. Vugalter) Weakly coupled bound states of Pauli operators. Calc. Var. Partial Differential Equations 40 (2010), no. 1 - 2, 253 - 271. Article - Preprint
  34. (with E.H. Lieb) Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality. Calc. Var. Partial Differential Equations 39 (2010), no. 1 - 2, 85 - 99. Article - Preprint
  35. (with R. Seiringer) Sharp fractional Hardy inequalities in half-spaces. In: Around the research of Vladimir Maz'ya, A. Laptev (ed.), 161 - 167, International Mathematical Series 11 (2010). Article - Preprint
  36. (with A. Laptev) Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Int. Math. Res. Not. 15 (2010), 2889 - 2902. Article - Preprint
  37. (with E.H. Lieb and R. Seiringer) Equivalence of Sobolev inequalities and Lieb-Thirring inequalities. In: XVIth International Congress on Mathematical Physics, Proceedings of the ICMP held in Prague, August 3-8, 2009, P. Exner (ed.), 523-535, World Scientific, Singapore, 2010. Article - Preprint
  38. (with B. Simon) Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices. Duke Math. J. 157 (2011), no. 3, 461 - 493. Article - Preprint
  39. (with E.H. Lieb) Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality. In: Concentration, Functional Inequalities and Isoperimetry, C. Houdré et al. (eds.), Contemp. Math. 545, Amer. Math. Soc., Providence, RI, 2011. Article - Preprint
  40. (with E.H. Lieb, R. Seiringer and L.E. Thomas) Bi-polaron and N-polaron binding energies. Phys. Rev. Lett. 104 (2010), 210402. Article - Preprint
  41. (with E.H. Lieb, R. Seiringer and L.E. Thomas) Stability and absence of binding for multi-polaron systems. Publ. Math. IHES 113 (2011), no. 1, 39 - 67. Article - Preprint
  42. Eigenvalue bounds for Schrödinger operators with complex potentials. Bull. Lond. Math. Soc. 43 (2011), no. 4, 745 - 750. Article - Preprint
  43. (with E.H. Lieb) Sharp constants in several inequalities on the Heisenberg group. Ann. of Math. 176 (2012), no. 1, 349 - 381. Article - Preprint
  44. (with E. Lenzmann) Uniqueness and nondegeneracy of ground states for (-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R. Acta Math. 210 (2013), no. 2, 261 - 318. Article - Preprint
  45. (with E.H. Lieb, R. Seiringer and L.E. Thomas) Binding, stability and non-binding of multi-polaron systems. In: Mathematical results in quantum physics, Proceedings of the QMath11 Conference, P. Exner (ed.), 21 - 32, World Scientific, Singapore, 2011. Article - Preprint
  46. (with L. Geisinger) Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain. In: Mathematical results in quantum physics, Proceedings of the QMath11 Conference, P. Exner (ed.), 138 - 147, World Scientific, Singapore, 2011. Article - Preprint
  47. (with E.H. Lieb) A new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality. In: Spectral Theory, Function Spaces and Inequalities, B. M. Brown et al. (eds.), 55 - 67, Oper. Theory Adv. Appl. 219, Birkhäuser, Basel, 2012. Article - Preprint
  48. (with D. Lenz and D. Wingert) Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory. J. Funct. Anal. 266 (2014), no. 8, 4765 - 4808. Article - Preprint
  49. (with R. Olofsson) Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field. Lett. Math. Phys. 97 (2011), no. 3, 227 - 241, Article - Preprint
  50. (with M. Lewin, E.H. Lieb and R. Seiringer) Energy cost to make a hole in the Fermi sea. Phys. Rev. Lett. 106 (2011), 150402. Article - Preprint
  51. (with C. Hainzl, R. Seiringer and J. P. Solovej) Microscopic derivation of Ginzburg-Landau theory. J. Amer. Math. Soc. 25 (2012), no. 3, 667 - 713. Article - Preprint
  52. (with M. Loss) Hardy-Sobolev-Maz'ya inequalities for arbitrary domains. J. Math. Pures Appl. 97 (2012), 39 - 54. Article - Preprint
  53. (with C. Hainzl, R. Seiringer and J. P. Solovej) Derivation of Ginzburg-Landau theory for a one-dimensional system with contact interaction. In: Operator Methods in Mathematical Physics, J. Janas et al. (eds.), 57 - 88, Oper. Theory Adv. Appl. 227, Birkhäuser, Basel, 2013. Article - Preprint
  54. (with E.H. Lieb) Possible lattice distortions in the Hubbard model for graphene. Phys. Rev. Lett. 107 (2011), 066801. Article - Preprint
  55. (with L. Geisinger) Refined semiclassical asymptotics for fractional powers of the Laplace operator. J. Reine Angew. Math. 712 (2016), 1 - 37. Article - Preprint
  56. (with E.H. Lieb and R. Seiringer) Binding of polarons and atoms at threshold. Comm. Math. Phys. 313 (2012), no. 2, 405 - 424. Article - Preprint
  57. (with H.D. Cornean, S. Fournais and B. Helffer) Sharp trace asymptotics for a class of 2D-magnetic operators. Ann. Inst. Fourier (Grenoble) 63 (2013), no. 6, 2457 - 2513. Article - Preprint
  58. (with M. Lewin, E.H. Lieb and R. Seiringer) A positive density analogue of the Lieb-Thirring inequality. Duke Math. J. 162 (2013), no. 3, 435 - 495. Article - Preprint
  59. (with H. Kovarik) Heat kernels of metric trees and applications. SIAM J. Math. Anal. 45 (2013), no. 3, 1027 - 1046. Article - Preprint
  60. (with E.H. Lieb) Entropy and the uncertainty principle. Ann. Henri Poincaré 13 (2012), no. 8, 1711 - 1717. Article - Preprint
  61. On the uniqueness of ground states of non-local equations. Journées Équations aux Dérivées Partielles 2011, Exp. No. V, 10 pp. Article - Preprint
  62. (with B. Dyda) Fractional Hardy-Sobolev-Maz'ya inequality for domains. Studia Math. 208 (2012), no. 2, 151 - 166. Article - Preprint
  63. (with R. Seiringer) Lieb-Thirring inequality for a model of particles with point interactions. J. Math. Phys. 53 (2012), no. 9, 095201. Article - Preprint
  64. (with E.H. Lieb and R. Seiringer) Symmetry of bipolaron bound states for small Coulomb repulsion. Comm. Math. Phys. 319 (2013), no. 2, 557 - 573. Article - Preprint
  65. (with E.H. Lieb) Extended quantum conditional entropy and quantum uncertainty inequalities. Comm. Math. Phys. 323 (2013), no. 2, 487 - 495. Article - Preprint
  66. (with S. Chen and T. Weth) Remainder terms in the fractional Sobolev inequality. Indiana Univ. Math. J. 62 (2013), 1381 - 1397. Article - Preprint
  67. Cwikel's theorem and the CLR inequality. J. Spectr. Theory 4 (2014), no. 1, 1 - 21. Article - Preprint
  68. (with L. Geisinger) Semi-classical analysis of the Laplace operator with Robin boundary conditions. Bull. Math. Sci. 2 (2012), no. 2, 281 - 319. Article - Preprint
  69. (with C. Hainzl, R. Seiringer and J. P. Solovej) Microscopic derivation of the Ginzburg-Landau model. In: XVIIth International Congress on Mathematical Physics, Proceedings of the ICMP held in Aalborg, August 6-11, 2012, A. Jensen (ed.), 575-583, World Scientific, Singapore, 2013. Article - Preprint
  70. (with E.H. Lieb, R. Seiringer and L.E. Thomas) Ground state properties of multi-polaron systems. In: XVIIth International Congress on Mathematical Physics, Proceedings of the ICMP held in Aalborg, August 6-11, 2012, A. Jensen (ed.), 477-485, World Scientific, Singapore, 2013. Article - Preprint
  71. (with E.A. Carlen and E.H. Lieb) Stability estimates for the lowest eigenvalue of a Schrödinger operator. Geom. Funct. Anal. 24 (2014), no. 1, 63 - 84. Article - Preprint
  72. (with J. Bellazzini, E.H. Lieb and R. Seiringer) Existence of ground states for negative ions at the binding threshold. Rev. Math. Phys. 26 (2014), no. 1, 1350021. Article - Preprint
  73. (with E. Lenzmann and L. Silvestre) Uniqueness of radial solutions for the fractional Laplacian. Comm. Pure Appl. Math. 69 (2016), no. 9, 1671 - 1726. Article - Preprint
  74. (with L. Geisinger) The ground state energy of a polaron in a strong magnetic field. Comm. Math. Phys. 338 (2015), no. 1, 1 - 29. Article - Preprint
  75. (with M. Lewin, E.H. Lieb and R. Seiringer) Strichartz inequality for orthonormal functions. J. Eur. Math. Soc. 16 (2014), no. 7, 1507 - 1526. Article - Preprint
  76. (with E.H. Lieb) Monotonicity of a relative Rényi entropy. J. Math. Phys. 54 (2013), 122201. Article - Preprint
  77. (with J. Bellazzini and N. Visciglia) Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems. Math. Ann. 360 (2014), no. 3-4, 653 - 673. Article - Preprint
  78. (with B. Schlein) Dynamics of a strongly coupled polaron. Lett. Math. Phys. 104 (2014), no. 8, 911 - 929. Article - Preprint
  79. (with M. d. M. Gonzalez, D. D. Monticelli and J. Tan) An extension problem for the CR fractional Laplacian. Adv. Math. 270 (2015), 97 - 137. Article - Preprint
  80. (with T. Ekholm and H. Kovarik) Weak perturbations of the p-Laplacian. Calc. Var. Partial Differential Equations 53 (2015), 781 - 801. Article - Preprint
  81. (with A. Pushnitski) Trace class conditions for functions of Schrödinger operators. Comm. Math. Phys. 335 (2015), 477 - 496. Article - Preprint
  82. (with J. Sabin) Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates. Amer. J. of Math. 139 (2017), no. 6, 1649 - 1691. Article - Preprint
  83. (with E. A. Carlen and E. H. Lieb) Some operator and trace function convexity theorems. Linear Algebra Appl. 490 (2016), 174 - 185. Article - Preprint
  84. (with A. Pushnitski) The spectral density of a product of spectral projections. J. Funct. Anal. 268 (2015), 3867 - 3894. Article - Preprint
  85. (with R. D. Benguria and E. H. Lieb) Ground state energy of large polaron systems. J. Math. Phys. 56 (2015), 021901. Article - Preprint
  86. (with C. Hainzl, R. Seiringer and J. P. Solovej) The external field dependence of the BCS critical temperature. Comm. Math. Phys. 342 (2016), no. 1, 189 - 216. Article - Preprint
  87. (with E. H. Lieb) A compactness lemma and its application to the existence of minimizers for the liquid drop model. SIAM J. Math. Anal. 47 (2015), no. 6, 4436 - 4450. Article - Preprint
  88. (with B. Simon) Eigenvalue bounds for Schrödinger operators with complex potentials. II. J. Spectr. Theory 7 (2017), no. 3, 633 - 658. Article - Preprint
  89. (with C. Hainzl, B. Schlein and R. Seiringer) Incompatibility of time-dependent Bogoliubov-de-Gennes and Ginzburg-Landau equations. Lett. Math. Phys. 106 (2016), no. 7, 913 - 923. Article - Preprint
  90. (with M. Lemm) Ginzburg-Landau theory with multiple order parameters: microscopic derivation and examples. Ann. H. Poincaré 17 (2016), no. 9, 2285 - 2340. Article - Preprint
  91. (with Z. Gang) Derivation of an effective evolution equation for a strongly coupled polaron. Anal. PDE 10 (2017), no. 2, 379 - 422. Article - Preprint
  92. Eigenvalue bounds for Schrödinger operators with complex potentials. III. Trans. Amer. Math. Soc. 370 (2018), no. 1, 219 - 240. Article - Preprint
  93. Eigenvalues of Schrödinger operators with complex surface potentials. In: Functional Analysis and Operator Theory for Quantum Physics, J. Dittrich, et al. (eds.), 245 - 260. EMS, 2017. Article - Preprint
  94. (with A. Laptev, O. Safronov) On the number of eigenvalues of Schrödinger operators with complex potentials. J. Lond. Math. Soc. (2) 94 (2016), no. 2, 377 - 390. Article - Preprint
  95. (with J. Behrndt, C. Kühn, V. Lotoreichik, J. Rohleder) Spectral theory for Schrödinger operators with δ-interactions supported on curves in R^3. Ann. H. Poincaré 18 (2017), no. 4, 1305 - 1347. Article - Preprint
  96. (with E. H. Lieb, J. Sabin) Maximizers for the Stein-Tomas inequality. Geom. Funct. Anal. 26 (2016), no. 4, 1095 - 1134. Article - Preprint
  97. Eigenvalue bounds for the fractional Laplacian: A review. In: Recent Developments in Nonlocal Theory, G. Palatucci, T. Kuusi (eds.), 210 - 235, De Gruyter, 2017. Article - Preprint
  98. (with R. Killip, P. T. Nam) Nonexistence of large nuclei in the liquid drop model. Lett. Math. Phys. 106 (2016), no. 8, 1033 - 1036. Article - Preprint
  99. (with P. T. Nam, H. Van Den Bosch) The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory. Comm. Pure Appl. Math. 71 (2018), no. 3, 577 - 614. Article - Preprint
  100. (with E. H. Lieb) A `liquid-solid' phase transition in a simple model for swarming, based on the “No Flat-Spots” theorem for subharmonic functions. Indiana Univ. Math. J. 67 (2018), no. 4, 1547 - 1569. Article - Preprint
  101. (with M. Lemm and B. Simon) Condensation of fermion pairs in a domain. Calc. Var. Partial Differential Equations 56 (2017), no. 2, 54. Article - Preprint
  102. (with P. T. Nam, H. Van Den Bosch) The maximal excess charge in Müller density-matrix-functional theory. Ann. H. Poincaré 19 (2018), no. 9, 2839 - 2867. Article - Preprint
  103. (with J. Sabin) Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Adv. Math. 317 (2017), 157 - 192. Article - Preprint
  104. (with J. Sabin) The Stein-Tomas inequality in trace ideals. Séminaire Laurent Schwartz - Équations aux dérivées partielles et applications. Année 2015 - 2016, Exp. No. XV, 12 pp., Ed. Éc. Polytech., Palaiseau, 2016. Article - Preprint
  105. (with L. Schimmer) Endpoint resolvent estimates for compact Riemannian manifolds. J. Funct. Anal. 272 (2017), no. 9, 3904 - 3918. Article - Preprint
  106. (with F. Méhats, C. Sparber) Averaging of nonlinear Schrödinger equations with strong magnetic confinement. Comm. Math. Sci. 15 (2017), no. 7, 1933 - 1945. Article - Preprint
  107. (with P. T. Nam, H. Van Den Bosch) A short proof of the ionization conjecture in Müller theory. In: Mathematical Problems in Quantum Physics, F. Bonetto, et al. (eds.), 1 - 12, Contemporary Mathematics 717, Amer. Math. Soc., 2018. Article - Preprint
  108. (with E. H. Lieb) Norms of quantum Gaussian multi-mode channels. J. Math. Phys. 58 (2017), 062204. Article - Preprint
  109. (with C. Hainzl, E. Langmann) The BCS critical temperature in a weak homogeneous magnetic field. J. Spectr. Theory 9 (2019), no. 3, 1005 - 1062. Article - Preprint
  110. (with T. Jin, J. Xiong) Minimizers for the fractional Sobolev inequality on domains. Calc. Var. Partial Differential Equations 57 (2018), no. 2, 57 - 43. Article - Preprint
  111. (with T. König) Classification of positive solutions to a nonlinear biharmonic equation with critical exponent. Anal. PDE 12 (2019), no. 4, 1101 - 1113. Article - Preprint
  112. (with A. Laptev) Bound on the number of negative eigenvalues of two-dimensional Schrödinger operators on domains. Algebra i Analiz 30 (2018), no. 3, 250 - 272. Reprinted in St. Petersburg Math. J. 30 (2019), no. 3, 573 - 589. Article - Preprint
  113. (with J. Sabin) Extremizers for the Airy-Strichartz inequality. Math. Ann. 372 (2018), no. 3-4, 1121 - 1166. Article - Preprint
  114. (with C. Hainzl) The BCS critical temperature in a weak external electric field via a linear two-body operator. In: D. Cadamuro, M. Duell, W. Dybalski, S. Simonella (eds), Macroscopic Limits of Quantum Systems. MaLiQS 2017. Springer Proceedings in Mathematics & Statistics, vol 270. Springer, Cham. Article - Preprint
  115. (with J. A. Carrillo, M. G. Delgadino, J. Dolbeault, F. Hoffmann) Reverse Hardy-Littlewood-Sobolev inequalities. J. Math. Pures Appl. (9) 132 (2019), 133 - 165. Article - Preprint, see also Preprint
  116. (with E. A. Carlen, E. H. Lieb) Inequalities for quantum divergences and the Audenaert-Datta conjecture. J. Phys. A 51 (2018), no. 48, 483001. Article - Preprint
  117. (with E. A. Carlen, P. Ivanisvili, E. H. Lieb) Inequalities for Lp-norms that sharpen the triangle inequality and complement Hanner's inequality. J. Geom. Anal. 31 (2021), no. 4, 4051 - 4073. Article - Preprint
  118. (with K. Merz, H. Siedentop) Equivalence of Sobolev norms involving generalized Hardy operators. Int. Math. Res. Not. 3 (2021), 2284 - 2303. Article - Preprint
  119. (with L. Emmert, T. König) Liquid drop model for nuclear matter in the dilute limit. SIAM J. Math. Anal. 52 (2020), no. 2, 1980 - 1999. Article - Preprint
  120. (with E. H. Lieb) Periodic energy minimizers for a one-dimensional liquid drop model. Lett. Math. Phys. 109 (2019), no. 9, 2069 - 2081. Article - Preprint
  121. (with D. Hundertmark, M. Jex, P. T. Nam) The Lieb-Thirring inequality revisited. J. Eur. Math. Soc. 23 (2021), no. 8, 2583 - 2600. Article - Preprint
  122. (with A. Borichev, A. Volberg) Counting eigenvalues of Schrödinger operators with fast decreasing complex potential. Adv. Math. 397 (2022), 108115. Article - Preprint
  123. (with W. Borrelli) Sharp decay estimates for critical Dirac equations. Trans. Amer. Math. Soc. 373 (2020), no. 3, 2045 - 2070. Article - Preprint
  124. (with A. Pushnitski) Kato smoothness and functions of perturbed self-adjoint operators. Adv. Math. 351 (2019), 343 – 387. Article - Preprint
  125. (with A. Pushnitski) Schatten class conditions for functions of Schrödinger operators. Ann. Henri Poincaré 20 (2019), no. 11, 3543 - 3562. Article - Preprint
  126. (with S. Larson) Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain. J. Reine Angew. Math. 766 (2020), 195 - 228. Article - Preprint
  127. (with R. Seiringer) Quantum corrections to the Pekar asymptotics of a strongly coupled polaron. Comm. Pure Appl. Math. 74 (2021), no. 3, 544 - 588. Article - Preprint
  128. (with E. A. Carlen and E. H. Lieb) Inequalities that sharpen the triangle inequality for sums of N functions in Lp. Ark. Mat. 58 (2020), no. 1, 57 - 69. Article - Preprint
  129. (with T. König) Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), no. 4, 817 - 846. Article - Preprint
  130. Non-spherical equilibrium shapes in the liquid drop model. J. Math. Phys. 60 (2019), 071506. Article - Preprint
  131. (with Z. Gang) A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations. J. Funct. Anal. 279 (2020), no. 7, 108631. Article - Preprint
  132. (with K. Merz, H. Siedentop and B. Simon) Proof of the strong Scott conjecture for Chandrasekhar atoms. Pure and Applied Functional Analysis 5 (2020), no. 6, 1319 - 1356. Article - Preprint
  133. (with T. König and H. Kovarik) Energy asymptotics in the three-dimensional Brezis-Nirenberg problem. Calc. Var. Partial Differential Equations 60 (2021), Article number 58. Article - Preprint
  134. (with S. Kim, A. Pistoia) Non-degeneracy for the critical Lane-Emden system. Proc. Amer. Math. Soc. 149 (2021), no. 1, 265 - 278. Article - Preprint
  135. (with E. H. Lieb) Proof of spherical flocking based on quantitative rearrangement inequalities. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XXII (2021), 1241 - 1263. Article - Preprint; see also the supplementary note
  136. (with T. König and H. Kovarik) Energy asymptotics in the Brezis-Nirenberg problem. The higher-dimensional case. Mathematics in Engineering 2 (2020), no. 1, 119 - 140. Article - Preprint
  137. (with S. Larson) On the error in the two-term Weyl formula for the Dirichlet Laplacian. J. Math. Phys. 61 (2020), 043504. Article - Preprint
  138. (with D. Gontier and M. Lewin) The nonlinear Schrödinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalities. Comm. Math. Phys. 384 (2021), 1783 - 1828. Article - Preprint
  139. The Lieb-Thirring inequalities: Recent results and open problems. In: Nine mathematical challenges: an elucidation, A. Kechris, et al. (eds.), 45 - 86, Proceedings of Symposia in Pure Mathematics 104, Amer. Math. Soc., Providence, RI, 2021. Article - Preprint
  140. (with T. König and H. Tang) Classification of solutions of an equation related to a conformal log Sobolev inequality. Adv. Math. 375 (2020), 107395. Article - Preprint
  141. (with J. Sabin) Sharp Weyl laws with singular potentials. Pure and Applied Analysis 5 (2023), no. 1, 85 - 144. Article - Preprint
  142. (with K. Merz and H. Siedentop) Relativistic strong Scott conjecture: a short proof. In: Density Functionals for Many-Particle Systems. Mathematical Theory and Physical Applications of Effective Equations, B.-G. Englert, et al. (eds.), Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 41, 69 - 79, World Scientific, Singapore, 2023. Article - Preprint
  143. (with D. Gontier and M. Lewin) The periodic Lieb-Thirring inequality. In: Partial Differential Equations, Spectral Theory, and Mathematical Physics. The Ari Laptev Anniversary Volume, P. Exner, et al. (eds.), 135 - 154, EMS Publishing House, 2021. Article - Preprint
  144. (with S. Larson) Semiclassical asymptotics for a class of singular Schrödinger operators. In: Partial Differential Equations, Spectral Theory, and Mathematical Physics. The Ari Laptev Anniversary Volume, P. Exner, et al. (eds.), 155 - 176, EMS Publishing House, 2021. Article - Preprint
  145. (with H. Chen and H. Siedentop) A statistical theory of heavy atoms: energy and excess charge. In: Density Functionals for Many-Particle Systems. Mathematical Theory and Physical Applications of Effective Equations, B.-G. Englert, et al. (eds.), Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 41, 57 - 68, World Scientific, Singapore, 2023. Article - Preprint
  146. (with S. Larson) Two consequences of Davies' Hardy inequality. Functional Analysis and Its Applications 55 (2021), no. 2, 174 - 177. (Translation of Funktsional. Anal. i Prilozhen 55 (2021), no. 2, 118 - 121) Article - Preprint
  147. (with J. A. Carrillo, M. G. Delgadino and M. Lewin) Fast diffusion leads to partial mass concentration in Keller-Segel type stationary solutions. M3AS 32 (2022), no. 4, 831 - 850. Article - Preprint
  148. (with M. Loss) Which magnetic fields support a zero mode? J. Reine Angew. Math. 788 (2022), 1 - 36. Article - Preprint
  149. (with P. T. Nam) Existence and nonexistence in the liquid drop model. Calc. Var. Partial Differential Equations 60 (2021), Article number: 223. Article - Preprint
  150. (with P. Ivanisvili) Hypercontractivity of the semigroup of the fractional laplacian on the n-sphere. J. Funct. Anal. 281 (2021), no. 8, 109145. Article - Preprint
  151. (with T. König and H. Kovarik) Blow-up of solutions of critical elliptic equation in three dimensions. Anal. PDE 17 (2024), no. 5, 1633 - 1692. Article - Preprint
  152. (with S. Larson) On the spectrum of the Kronig-Penney model in a constant electric field. Probab. Math. Phys. 3 (2022), no. 2, 431 - 490. Article - Preprint
  153. (with T. König and H. Tang) Reverse conformally invariant Sobolev inequalities on the sphere. J. Funct. Anal. 282 (2022), no. 4, 109339. Article - Preprint
  154. (with J. Dolbeault and L. Jeanjean) Logarithmic estimates for mean-field models in dimension two and the Schrödinger-Poisson system. Comptes Rendus Mathématique 359 (2021), no. 10, 1279 - 1293. Article - Preprint
  155. (with M. Loss) Existence of optimizers in a Sobolev inequality for vector fields. Ars Inveniendi Analytica (2022), Paper No. 1. Article - Preprint
  156. Degenerate stability of some Sobolev inequalities. Ann. Inst. H. Poincaré Anal. Non Linéaire 39 (2022), no. 6, 1459 - 1484. Article - Preprint
  157. (with S. Larson) Discrete Schrödinger operators with decaying and oscillating potentials. Algebra & Analiz 35 (2023), no. 1, 304 - 320. Article - Translation: St. Petersburg Math. J. 35 (2024), 233 - 244. Article - Preprint
  158. Some minimization problems for mean field models with competing forces. In: Proceedings of the 8th Congress (8ECM) held in Portoroz, 20 - 26 June 2021. Edited by A. Hujdurovic et al., EMS Press, Berlin, 2023, 277 - 294. Article - Preprint
  159. (with D. Gontier and M. Lewin) Optimizers for the finite-rank Lieb-Thirring inequality. Amer. J. Math. 147 (2025), no. 2, 503 - 560. Article - Preprint
  160. Minimizers for a one-dimensional interaction energy. Nonlinear Anal. 216 (2022), Paper No. 112691. Article - Preprint
  161. Lieb-Thirring inequalities and other functional inequalities for orthonormal systems. In: Proc. Int. Cong. Math. 2022, EMS Press, Berlin, 2023; Vol. 5, pp. 3756 - 3774. Article - Preprint
  162. (with M. Loss) A sharp criterion for zero modes of the Dirac equation. J. Eur. Math. Soc. 28 (2026), no. 1, 305 - 331. Article - Preprint
  163. (with S. Larson) An inequality for the normal derivative of the Lane-Emden ground state. Advances in Calculus of Variations 17 (2024), no. 2, 255 - 276. Article - Preprint
  164. Weyl's law under minimal assumptions. In: Operator Theory: Advances and Applications, M. Brown et al. (eds.), 549 - 572, Birkhäuser, Basel, 2023. Article - Preprint
  165. A characterization of Ẇ1,p(Rd). Pure Appl. Funct. Anal. 9 (2024), no. 1, 53 - 67. Article - Preprint
  166. (with A. Laptev and T. Weidl) An improved one-dimensional Hardy inequality. Journal of Mathematical Sciences 268 (2022), 323 - 342. Article - Preprint
  167. (with K. Merz and H. Siedentop) The Scott conjecture for large Coulomb systems: a review. Lett. Math. Phys. 113 (2023), Article number: 11. Article - Preprint
  168. The work of Elliott Lieb. In: Proc. Int. Cong. Math. 2022, EMS Press, Berlin, 2023; pp. 142 - 158. Article - Preprint
  169. Rearrangement methods in the work of Elliott Lieb. In: The Physics and Mathematics of Elliott Lieb. The 90th Anniversary Volume I, R. L. Frank, et al. (eds.), 351 - 375, EMS Publishing House, 2022. Article - Preprint
  170. (with J. Dolbeault, M. Esteban, A. Figalli and M. Loss) Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence. Camb. J. Math. 13 (2025), no. 2, 359 - 430. Article - Preprint
  171. (with F. Sukochev and D. Zanin) Asymptotics of singular values for quantum derivatives. Trans. Amer. Math. Soc. 376 (2023), no. 3, 2047 - 2088. Article - Preprint
  172. Sharp inequalities for coherent states and their optimizers. Advanced Nonlinear Studies 23 (2023), no. 1, Paper No. 20220050, 28 pp. Article - Preprint
  173. (with A. Laptev and T. Weidl) Schrödinger operators: Eigenvalues and Lieb-Thirring Inequalities. Cambridge Studies in Advanced Mathematics 200, Cambridge University Press, Cambridge, 2023. Book
  174. (with F. Sukochev and D. Zanin) Endpoint Schatten class properties of commutators. Adv. Math. 450 (2024), Paper No. 109738, 53 pp. Article - Preprint
  175. (with K. Merz) On Sobolev norms involving Hardy operators in a half-space. J. Funct. Anal. 285 (2023), no. 10, Paper No. 110104, 54 pp. Article - Preprint
  176. (with A. Laptev and L. Read) Weighted CLR type bounds in two dimensions. Trans. Amer. Math. Soc. 377 (2024), no. 5, 3357 - 3371. Article - Preprint
  177. The sharp Sobolev inequality and its stability: An introduction. In: Lecture Notes in Math., 2348 CIME Found. Subser. Springer, Cham, 2024, 1–64. Article - Preprint
  178. (with R. Matzke) Minimizers for an aggregation model with attractive-repulsive interaction. Arch. Ration. Mech. Anal. 249 (2025), no. 2, Paper No. 15, 28 pp. Article - Preprint
  179. (with F. Nicola and P. Tilli) The generalized Wehrl entropy bound in quantitative form. J. Eur. Math. Soc., published online first. Article - Preprint
  180. (with S. Fournais, M. Goffeng, A. Kachmar and M. Sundqvist) Counting negative eigenvalues for the magnetic Pauli operator. Duke Math. J. 174 (2025), no. 2, 313 - 353. Article - Preprint
  181. (with J. Peteranderl) Degenerate stability of the Caffarelli-Kohn-Nirenberg inequality along the Felli--Schneider curve. Calc. Var. Partial Differential Equations 63 (2024), no. 2, Paper No. 44, 33 pp. Article - Preprint
  182. A div-curl inequality for orthonormal functions. Pure Appl. Funct. Anal. 9 (2024), no. 4, 1081 - 1091. Article - Preprint
  183. (with G. K. Duong, T. M. T. Le, P. T. Nam and P.-T. Nguyen) Cwikel-Lieb-Rozenblum type inequalities for Hardy-Schrödinger operator. J. Math. Pures Appl. (9) 190 (2024), Paper No. 103598, 16 pp. Article - Preprint
  184. (with B. Helffer) On Courant and Pleijel theorems for sub-Riemannian Laplacians. J. Éc. polytech. Math. 12 (2025), 1083 - 1160. Article - Preprint
  185. (with B. Helffer) On Courant and Pleijel theorems for sub-Riemannian Laplacians In: Trends Math., Res. Perspect. Ghent Anal. PDE Cent., 8, Birkhäuser/Springer, Cham, 2025, 9 - 23. Article
  186. (with T. Jin and W. Wang) On the sharp constants in the regional fractional Sobolev inequalities. Partial Differ. Equ. Appl. 6 (2025), no. 2, Paper No. 15, 20 pp. Article - Preprint
  187. (with T. Hoffmann-Ostenhof, A. Laptev and J. P. Solovej) Hardy inequalities for large fermionic systems. J. Spectr. Theory 14 (2024), no. 2, 805 - 835. Article - Preprint
  188. (with H. Kovarik) Lieb-Thirring inequality for the 2D Pauli operator. Comm. Math. Phys. 406 (2025), no. 2, Paper No. 23, 38 pp. Article - Preprint
  189. (with S. Larson) Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains. Invent. Math. 241 (2025), no. 3, 999 - 1079. Article - Preprint
  190. Minimizing Schrödinger eigenvalues for confining potentials. Advanced Nonlinear Studies 25 (2025), no. 4, 1025 - 1031. Article - Preprint
  191. (with S. Larson) Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains. Comm. Pure Appl. Math. 79 (2026), no. 3, 762 - 822. Article - Preprint
  192. (with S. Larson) Spectral asymptotics for Robin Laplacians on Lipschitz sets. Funktsional. Anal. i Prilozhen 59 (2025), no. 3, 71 - 95. Article - Preprint
  193. (with B. Helffer and A. Laptev) Inequalities between Dirichlet and Neumann eigenvalues on Carnot groups. Pure Appl. Funct. Anal., to appear. Preprint
  194. (with J. W. Peteranderl) The sharp σ2-curvature inequality on the sphere in quantitative form. Submitted. Preprint
  195. (with S. Larson and P. Pfeiffer) Improved semiclassical eigenvalue estimates for the Laplacian and the Landau Hamiltonian. J. Spectr. Theory 16 (2026), no. 1, 243 - 270. Article - Preprint
  196. (with E. A. Carlen and S. Larson) A Jensen inequality for partial traces and applications to partially semiclassical limits. Lett. Math. Phys. 115 (2025), no. 3, Paper No. 52, 15 pp. Article - Preprint
  197. (with J. Mateu, M. G. Mora, L. Rondi, L. Scardia and J. Verdera) Explicit minimisers for anisotropic Riesz energies. Calc. Var. Partial Differential Equations 65 (2026), no. 1, Paper No. 34. Article - Preprint
  198. (with J. Dolbeault, M. Esteban and M. Loss) The CKN inequality for spinors: symmetry and symmetry breaking. J. Math. Pures Appl. 215 (2026), Paper No. 103958. Article - Preprint
  199. (with M. Lewin and R. Seiringer) Liquid drop model for nuclear matter in the low density limit. Comm. Pure Appl. Math. (2026), published online first. Article - Preprint
  200. (with J. W. Peteranderl and L. Read) Sharp quantitative integral inequalities for harmonic extensions. Ann. Sc. Norm. Super. Pisa Cl. Sci. (2026), published online first, 39 pp. Article - Preprint
  201. (with A. Laptev and D. Suragan) Eigenvalue lower bounds through a generalized inradius. J. Funct. Anal. 291 (2026), no. 1, Paper No. 111473. Article - Preprint
  202. Openness of shape optimizers in higher-order and non-scalar problems. Interfaces Free Bound. (2026), published online first. Article - Preprint
  203. (with L. Read) Jost solutions and direct scattering for the continuum Calogero-Moser equation. Proceedings of the London Math. Soc., to appear. Preprint
  204. (with S. Larson) Uniform bounds for Neumann heat kernels and their traces in convex sets. Preprint (2026). Preprint
  205. (with K. Merz) Sharp upper bounds for the density of relativistic atoms: Noninteracting case. Pure Appl. Funct. Anal., to appear. Preprint
  206. (with S. Larson) An asymptotic shape optimization problem for Riesz means of Laplacian eigenvalues. Preprint (2026). Preprint
  207. (with L. Meng, P. T. Nam and H. Siedentop) Eigenvalue asymptotics of Müller minimizers for atoms and molecules. Preprint (2026). Preprint
  208. (with C. Hainzl and D. H. Ou Yang) From Bogoliubov-de Gennes to Ginzburg-Landau: Critical Points Near Tc in the Non-Magnetic Case. Preprint (2026). Preprint
  209. (with P. Ivanisvili) The sharp log Sobolev inequality on finite cycles. Adv. Math. 502 (2026), Part B, Paper No. 111159. Article - Preprint
  210. (with B. Helffer) Pleijel's theorem for a class of degenerate elliptic operators. Int. Math. Res. Not. (2026), no. 20, Paper No. rnag220. Article - Preprint
  211. (with P. Koskela and R. Mishra) Sobolev extensions, interpolation inequalities and consequences. Preprint (2026). Preprint
  212. (with P. Ivanisvili) The sharp extension norm for a planar sector. Preprint (2026). Preprint
  213. (with P. Ivanisvili and C. Torres-Latorre) Minimizers for Coulomb gases constrained to a halfspace. Preprint (2026). Preprint
  214. (with P. Ivanisvili) The distance between homotopy classes of Sobolev maps on spheres. Preprint (2026). Preprint
  215. (with Y. Li and D. Yang) Stability for the Affine Sobolev Inequality and its Critical Points for p ≥ 2. Preprint (2026). Preprint
  216. (with P. Ivanisvili) The Winding Number at the Critical Hölder Exponent 1/3: Failure of Universal Fourier Summation. Preprint (2026). Preprint
  217. (with P. Ivanisvili) Counterexamples to the Landis conjecture in dimensions three and higher. Preprint (2026). Preprint
  218. (with P. Ivanisvili) A counterexample to the Kato conjecture for positive commutators. Preprint (2026). Preprint
  219. (with M. del Pino and M. Musso) The double sphere solution in the liquid drop model. Preprint (2026). Preprint
  220. (with P. Ivanisvili) Sharp comparison between the perimeter and its fractional analogue in two dimensions. Preprint (2026). Preprint
  221. Another characterization of Ẇ1,p(Rd). Preprint (2026). Preprint
  222. (with P. Ivanisvili) The sharp constant in the Chang--Marshall inequality. Preprint (2026). Preprint
  223. (with T. Jin, H.-Y. Wang and J. Xiong) Sharp Sobolev inequalities under first moment constraints. Preprint (2026). Preprint

Unpublished manuscripts

  1. (with E. Lenzmann) On ground states for the L2-critical boson star equation. Manuscript
  2. (with E. H. Lieb) A note on a theorem of M. Christ. Manuscript
  3. (with J. C. Cuenin) Open problem: Violation of locality for Schrödinger operators with complex potentials. Manuscript
  4. (with J. Dolbeault and J. Weixler) Symmetry and symmetry breaking in interpolation inequalities for two-dimensional spinors - Preliminary results. Manuscript


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Last modified: October 17, 2026