List of Publications:
- On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators. Doc. Math. 8 (2003), 547 - 565. Article
- (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
- On the Laplacian in the halfspace with a periodic boundary condition. Ark. Mat. 44 (2006), no. 2, 277 - 298. Article - Preprint
- On the tunneling effect for magnetic Schrödinger operators in antidot lattices. Asymptot. Anal. 48 (2006), no. 1-2, 91 - 120. Article - Preprint
- (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
- (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
- (with P. Exner) Absolute continuity of the spectrum for periodically modulated leaky wires in R^3. Ann. Henri Poincaré 8 (2007), no. 2, 241 - 263. Article - Preprint
- (with T. Ekholm) On Lieb-Thirring inequalities for Schrödinger operators with virtual level. Comm. Math. Phys. 264 (2006), no. 3, 725 - 740. Article - Preprint
- On the asymptotic number of edge states for magnetic Schrödinger operators. Proc. London Math. Soc. (3) 95 (2007), no. 1, 1 - 19. Article - Preprint
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (with T. Ekholm and H. Kovarik) Eigenvalue estimates for Schrödinger operators on metric trees. Adv. Math. 226 (2011), 5165 - 5197. Article - Preprint
- (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. Preprint
- (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). Preprint
- (with R. Seiringer) Non-linear ground state representations and sharp Hardy inequalities. J. Funct. Anal. 255 (2008), 3407 - 3430. Article - Preprint
- (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
- (with J. Breuer) Singular spectrum for radial trees. Rev. Math. Phys. 21 (2009), no. 7, 1 - 17. Article - Preprint
- A simple proof of Hardy-Lieb-Thirring inequalities. Comm. Math. Phys. 290 (2009), no. 2, 789 - 800. Article - Preprint
- A note on low energy scattering for homogeneous long-range potentials. Ann. Henri Poincaré 10 (2009), no. 3, 573 - 575. Article - Preprint
- 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. Preprint
- (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
- (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
- (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
- (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
- (with A. Laptev) Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group. Int. Math. Res. Not. 15 (2010), 2889 - 2902. Article - Preprint
- (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
- (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
- (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
- (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
- (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
- Eigenvalue bounds for Schrödinger operators with complex potentials. Bull. Lond. Math. Soc. 43 (2011), no. 4, 745 - 750. Article - Preprint
- (with E.H. Lieb) Sharp constants in several inequalities on the Heisenberg group. Ann. of Math. 176 (2012), no. 1, 349 - 381. Article - Preprint
- (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
- (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
- (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
- (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
- (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
- (with R. Olofsson) Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field. Lett. Math. Phys. 97 (2011), no. 3, 227 - 241, Article - Preprint
- (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
- (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
- (with M. Loss) Hardy-Sobolev-Maz'ya inequalities for arbitrary domains. J. Math. Pures Appl. 97 (2012), 39 - 54. Article - Preprint
- (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
- (with E.H. Lieb) Possible lattice distortions in the Hubbard model for graphene. Phys. Rev. Lett. 107 (2011), 066801. Article - Preprint
- (with L. Geisinger) Refined semiclassical asymptotics for fractional powers of the Laplace operator. J. Reine Angew. Math. 712 (2016), 1 - 37. Article - Preprint
- (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
- (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
- (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
- (with H. Kovarik) Heat kernels of metric trees and applications. SIAM J. Math. Anal. 45 (2013), no. 3, 1027 - 1046. Article - Preprint
- (with E.H. Lieb) Entropy and the uncertainty principle. Ann. Henri Poincaré 13 (2012), no. 8, 1711 - 1717. Article - Preprint
- On the uniqueness of ground states of non-local equations. Journées Équations aux Dérivées Partielles 2011, Exp. No. V, 10 pp. Article - Preprint
- (with B. Dyda) Fractional Hardy-Sobolev-Maz'ya inequality for domains. Studia Math. 208 (2012), no. 2, 151 - 166. Article - Preprint
- (with R. Seiringer) Lieb-Thirring inequality for a model of particles with point interactions. J. Math. Phys. 53 (2012), no. 9, 095201. Article - Preprint
- (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
- (with E.H. Lieb) Extended quantum conditional entropy and quantum uncertainty inequalities. Comm. Math. Phys. 323 (2013), no. 2, 487 - 495. Article - Preprint
- (with S. Chen and T. Weth) Remainder terms in the fractional Sobolev inequality. Indiana Univ. Math. J. 62 (2013), 1381 - 1397. Article - Preprint
- Cwikel's theorem and the CLR inequality. J. Spectr. Theory 4 (2014), no. 1, 1 - 21. Article - Preprint
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (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
- (with E.H. Lieb) Monotonicity of a relative Rényi entropy. J. Math. Phys. 54 (2013), 122201. Article - Preprint
- (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
- (with B. Schlein) Dynamics of a strongly coupled polaron. Lett. Math. Phys. 104 (2014), no. 8, 911 - 929. Article - Preprint
- (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
- (with T. Ekholm and H. Kovarik) Weak perturbations of the p-Laplacian. Calc. Var. Partial Differential Equations 53 (2015), 781 - 801. Article - Preprint
- (with A. Pushnitski) Trace class conditions for functions of Schrödinger operators. Comm. Math. Phys. 335 (2015), 477 - 496. Article - Preprint
- (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
- (with E. A. Carlen and E. H. Lieb) Some operator and trace function convexity theorems. Linear Algebra Appl. 490 (2016), 174 - 185. Article - Preprint
- (with A. Pushnitski) The spectral density of a product of spectral projections. J. Funct. Anal. 268 (2015), 3867 - 3894. Article - Preprint
- (with R. D. Benguria and E. H. Lieb) Ground state energy of large polaron systems. J. Math. Phys. 56 (2015), 021901. Article - Preprint
- (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
- (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
- (with B. Simon) Eigenvalue bounds for Schrödinger operators with complex potentials. II. J. Spectr. Theory 7 (2017), no. 3, 633 - 658. Article - Preprint
- (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
- (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
- (with Z. Gang) Derivation of an effective evolution equation for a strongly coupled polaron. Anal. PDE 10 (2017), no. 2, 379 - 422. Article - Preprint
- Eigenvalue bounds for Schrödinger operators with complex potentials. III. Trans. Amer. Math. Soc. 370 (2018), no. 1, 219 - 240. Article - Preprint
- 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
- (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
- (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
- (with E. H. Lieb, J. Sabin) Maximizers for the Stein-Tomas inequality. Geom. Funct. Anal. 26 (2016), no. 4, 1095 - 1134. Article - Preprint
- 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
- (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
- (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
- (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
- (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
- (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
- (with J. Sabin) Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces. Adv. Math. 317 (2017), 157 - 192. Article - Preprint
- (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
- (with L. Schimmer) Endpoint resolvent estimates for compact Riemannian manifolds. J. Funct. Anal. 272 (2017), no. 9, 3904 - 3918. Article - Preprint
- (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
- (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
- (with E. H. Lieb) Norms of quantum Gaussian multi-mode channels. J. Math. Phys. 58 (2017), 062204. Article - Preprint
- (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
- (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
- (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
- (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
- (with J. Sabin) Extremizers for the Airy-Strichartz inequality. Math. Ann. 372 (2018), no. 3-4, 1121 - 1166. Article - Preprint
- (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
- (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
- (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
- (with E. A. Carlen, P. Ivanisvili, E. H. Lieb) Inequalities for L^{p}-norms that sharpen the triangle inequality and complement Hanner's inequality. J. Geom. Anal. 31 (2021), no. 4, 4051 - 4073. Article - Preprint
- (with K. Merz, H. Siedentop) Equivalence of Sobolev norms involving generalized Hardy operators. Int. Math. Res. Not. 3 (2021), 2284 - 2303. Article - Preprint
- (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
- (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
- (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
- (with A. Borichev, A. Volberg) Counting eigenvalues of Schrödinger operators with fast decreasing complex potential. Adv. Math. 397 (2022), 108115. Article - Preprint
- (with W. Borrelli) Sharp decay estimates for critical Dirac equations. Trans. Amer. Math. Soc. 373 (2020), no. 3, 2045 - 2070. Article - Preprint
- (with A. Pushnitski) Kato smoothness and functions of perturbed self-adjoint operators. Adv. Math. 351 (2019), 343 – 387. Article - Preprint
- (with A. Pushnitski) Schatten class conditions for functions of Schrödinger operators. Ann. Henri Poincaré 20 (2019), no. 11, 3543 - 3562. Article - Preprint
- (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
- (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
- (with E. A. Carlen and E. H. Lieb) Inequalities that sharpen the triangle inequality for sums of N functions in L^{p}. Ark. Mat. 58 (2020), no. 1, 57 - 69. Article - Preprint
- (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
- Non-spherical equilibrium shapes in the liquid drop model. J. Math. Phys. 60 (2019), 071506. Article - Preprint
- (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
- (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
- (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
- (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
- (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
- (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
- (with S. Larson) On the error in the two-term Weyl formula for the Dirichlet Laplacian. J. Math. Phys. 61 (2020), 043504. Article - Preprint
- (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
- 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
- (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
- (with J. Sabin) Sharp Weyl laws with singular potentials. Pure and Applied Analysis, to appear. Preprint
- (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
- (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
- (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
- (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
- (with S. Larson) Two consequences of Davies' Hardy inequality. Functional Analysis and Its Applications 55 (2021), no. 2, 174 - 177. (Translation of Translation of Funktsional. Anal. i Prilozhen 55 (2021), no. 2, 118 - 121) Article - Preprint
- (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
- (with M. Loss) Which magnetic fields support a zero mode? J. Reine Angew. Math. 788 (2022), 1 - 36. Article - Preprint
- (with P. T. Nam) Existence and nonexistence in the liquid drop model. Calc. Var. Partial Differential Equations 60 (2021), Article number: 223. Article - Preprint
- (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
- (with T. König and H. Kovarik) Blow-up of solutions of critical elliptic equation in three dimensions. Anal. PDE, to appear. Preprint
- (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
- (with T. König and H. Tang) Reverse conformally invariant Sobolev inequalities on the sphere. J. Funct. Anal. 282 (2022), no. 4, 109339. Article - Preprint
- (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
- (with M. Loss) Existence of optimizers in a Sobolev inequality for vector fields. Ars Inveniendi Analytica (2022), Paper No. 1. Article - Preprint
- Degenerate stability of some Sobolev inequalities. Ann. Inst. H. Poincaré Anal. Non Linéaire 39 (2022), no. 6, 1459 - 1484. Article - Preprint
- (with S. Larson) Discrete Schrödinger operators with decaying and oscillating potentials. Algebra & Analiz, to appear. Preprint
- Some minimization problems for mean field models with competing forces. Submitted. Preprint
- (with D. Gontier and M. Lewin) Optimizers for the finite-rank Lieb-Thirring inequality. Submitted. Preprint
- Minimizers for a one-dimensional interaction energy. Nonlinear Anal. 216 (2022), Paper No. 112691. Article - Preprint
- Lieb-Thirring inequalities and other functional inequalities for orthonormal systems. Submitted. Preprint
- (with M. Loss) A sharp criterion for zero modes of the Dirac equation. J. Eur. Math. Soc., to appear. Preprint
- (with S. Larson) An inequality for the normal derivative of the Lane-Emden ground state. Advances in Calculus of Variations, to appear. Article - Preprint
- Weyl's law under minimal assumptions. In: From Complex Analysis to Operator Theory: A Panorama. M Brown, et al. (eds.), to appear. Preprint
- A characterization of \dot W^{1,p}(R^d). Pure and Applied Functional Analysis, to appear. Preprint
- (with A. Laptev and T. Weidl) An improved one-dimensional Hardy inequality. Journal of Mathematical Sciences 268 (2022), 323 - 342. Article - Preprint
- (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
- The work of Elliott Lieb. Submitted. Preprint
- 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
- (with J. Dolbeault, M. Esteban, A. Figalli and M. Loss) Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence. Submitted. Preprint
- (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
- Sharp inequalities for coherent states and their optimizers. Advanced Nonlinear Studies, to appear. Preprint
- (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
- (with K. Merz) On Sobolev norms involving Hardy operators in a half-space. Submitted. Preprint
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