Rupert L. Frank
Rupert works in Analysis, PDE and Mathematical Physics. His research aims at developing new mathematical tools that enhance our qualitative and quantitative understanding of complex phenomena occurring in nature. Of particular interest are problems related to Quantum Physics.
Some recorded talks:
Lieb-Thirring bounds and other inequalities for orthonormal functions (Probability and Analysis Webinair, February 22, 2021)
Which magnetic fields support a zero mode? (Geometric Analysis Seminar, January 12, 2021)
Inequalities for L^p norms that sharpen the triangle inequality (Corona Seminar, December 10, 2020)
Recent results and open problems on Lieb-Thirring inequalities (Math Phys Seminar, Rutgers, November 18, 2020)
Minimal magnetic fields supporting a zero mode (Ari Laptev's 70th birthday conference, August 12, 2020)
Sharp Weyl Laws in 3d with rough potentials (Spectral geometry in the clouds Seminar, July 6, 2020)
A `liquid-solid' phase transition in a simple model for swarming (One World PDE Seminar, June 2, 2020)
Minicourse: A microscopic derivation of Ginzburg-Landau theory Part I, Part II, Part III (IHES, July 2016)
Stability estimates for the lowest eigenvalue of a Schrödinger operator (Banff, August 1, 2013)
Uniqueness and Nondegeneracy of Ground States for Non-Local Equations (Institute of Advanced Study, Princeton, October 19, 2012)
Editorial activity
Communications in Contemporary Mathematics
Selected 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 (-Δ)s Q + Q - Qα+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) Time-dependent Bogolubov-de-Gennes equations and non-validity of Ginzburg-Landau theory. 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 and 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 and J. Rohleder) Spectral theory for Schrödinger operators with δ-interactions supported on curves in R3. Ann. H. Poincaré 18 (2017), no. 4, 1305 - 1347. Article - Preprint
- (with E. H. Lieb and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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
- (with K. Merz and H. Siedentop) Equivalence of Sobolev norms involving generalized Hardy operators. Int. Math. Res. Not. 3 (2021), 2284 - 2303. Article - Preprint
- (with L. Emmert and 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 and P. T. Nam) The Lieb-Thirring inequality revisited. J. Eur. Math. Soc., to appear. Preprint
- (with A. Borichev and A. Volberg) Counting eigenvalues of Schrödinger operator with complex fast decreasing potential. Submitted. 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 Lp. 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 and 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), to appear. 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. 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., to appear. Preprint
- The Lieb-Thirring inequalities: Recent results and open problems. In: Linde Hall Inaugural Math Symposium, A. Kechris, et al. (eds.), Proceedings of Symposia in Pure Mathematics, Amer. Math. Soc., to appear. 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. Submitted. Preprint
- (with K. Merz and H. Siedentop) Relativistic strong Scott conjecture: a short proof. Submitted. 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.). EMS Publishing House, to appear. 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.). EMS Publishing House, to appear. Preprint
- (with H. Chen and H. Siedentop) A statistical theory of heavy atoms: energy and excess charge. Submitted. Preprint
- (with S. Larson) Two consequences of Davies's Hardy inequality. Functional Analysis and Its Applications, to appear. Preprint
- (with J. A. Carrillo, M. G. Delgadino and M. Lewin) Fast diffusion leads to partial mass concentration in Keller-Segel type stationary solutions. Submitted. Preprint
- (with M. Loss) Which magnetic fields support a zero mode? Submitted. Preprint
- (with P. T. Nam) Existence and nonexistence in the liquid drop model. Submitted. Preprint
- (with P. Ivanisvili) Hypercontractivity of the semigroup of the fractional laplacian on the n-sphere. Submitted. Preprint
- (with T. König and H. Kovarik) Blow-up of solutions of critical elliptic equation in three dimensions. Submitted. Preprint