Inventiones mathematicae

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• First order rigidity of non-uniform higher rank arithmetic groups AI翻译
  作者：Avni, Nir; Lubotzky, Alexander; Meiri, Chen
  作者单位：Northwestern University; Hebrew University of Jerusalem; Technion Israel Institute of Technology
  摘要：If is an irreducible non-uniform higher-rank characteristic zero arithmetic lattice (for example SLn(Z), n3) and is a finitely generated group that is elementarily equivalent to , then is isomorphic to Gamma.
• On the fine structure of the free boundary for the classical obstacle problem AI翻译
  作者：Figalli, Alessio; Serra, Joaquim
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：In the classical obstacle problem, the free boundary can be decomposed into regular and singular points. As shown by Caffarelli in his seminal papers (Caffarelli in Acta Math 139:155-184, 1977; J Fourier Anal Appl 4:383-402, 1998), regular points consist of smooth hypersurfaces, while singular points are contained in a stratified union of C1 manifolds of varying dimension. In two dimensions, this C1 result has been improved to C1, by Weiss (Invent Math 138:23-50, 1999). In this paper we prove ...
• Nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics AI翻译
  作者：Carrillo, J. A.; Hittmeir, S.; Volzone, B.; Yao, Y.
  作者单位：Imperial College London; University of Vienna; Parthenope University Naples; University System of Georgia; Georgia Institute of Technology
  摘要：We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially decreasing equilibrium configurations for all masses. All stationary states with suitable regularity are shown to be radially symmetric by means of continuous Steiner symmetrization techniques. Calculus of variations tools allow us to show the existence of glo...
• The derivation of the T3 energy-critical NLS from quantum many-body dynamics AI翻译
  作者：Chen, Xuwen; Holmer, Justin
  作者单位：University of Rochester; Brown University
  摘要：We derive the 3D energy critical quintic NLS from quantum many-body dynamics with 3-body interaction in the T3 (periodic) setting. Due to the known complexity of the energy critical setting, previous progress was limited in comparison to the 2-body interaction case yielding energy subcritical cubic NLS. Previously, the only result for the 3D energy critical case was Hong et al. (J Funct Anal 270(1):34-67, 2016), which proved the uniqueness part of the argument in the case of small solutions. I...
• The extension problem of the mean curvature flow (I) AI翻译
  作者：Li, Haozhao; Wang, Bing
  作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; Chinese Academy of Sciences; University of Science & Technology of China, CAS
  摘要：We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow IN R-3
• The Ax-Schanuel conjecture for variations of Hodge structures AI翻译
  作者：Bakker, Benjamin; Tsimerman, Jacob
  作者单位：University System of Georgia; University of Georgia; University of Toronto
  摘要：We extend the Ax-Schanuel theorem recently proven for Shimura varieties by Mok-Pila-Tsimerman to all varieties supporting a pure polarizable integral variation of Hodge structures. In fact, Hodge theory provides a number of conceptual simplifications to the argument. The essential new ingredient is a volume bound for Griffiths transverse subvarieties of period domains.
• Energy identity for stationary Yang Mills AI翻译
  作者：Naber, Aaron; Valtorta, Daniele
  作者单位：Northwestern University; University of Zurich
  摘要：Given a principal bundle PM over a Riemannian manifold with compact structure group G, let us consider a stationary Yang-Mills connection A with energy M|FA|2. If we consider a sequence of such connections Ai, then it is understood by Tian (Ann Math 151(1):193-268, 2000) that up to subsequence we can converge AiA to a singular limit connection such that the energy measures converge |FAi|2dvg|FA|2dvg+, where =e(x)dn-4 is the n-4 rectifiable defect measure. Our main result is to show, without ad...
• Riemann-Hilbert problems from Donaldson-Thomas theory AI翻译
  作者：Bridgeland, Tom
  作者单位：University of Sheffield
  摘要：We study a class of Riemann-Hilbert problems arising naturally in Donaldson-Thomas theory. In certain special cases we show that these problems have unique solutions which can be written explicitly as products of gamma functions. We briefly explain connections with Gromov-Witten theory and exact WKB analysis.
• Matrix group integrals, surfaces, and mapping class groups I: U(n) AI翻译
  作者：Magee, Michael; Puder, Doron
  作者单位：Durham University; Tel Aviv University
  摘要：Since the 1970's, physicists and mathematicians who study random matrices in the GUE or GOE models are aware of intriguing connections between integrals of such random matrices and enumeration of graphs on surfaces. We establish a new aspect of this theory: for random matrices sampled from the group U (n) of unitary matrices. More concretely, we study measures induced by free words on U (n). Let F-r be the free group on r generators. To sample a random element from U (n) according to the measu...
• Algebraic integrability of foliations with numerically trivial canonical bundle AI翻译
  作者：Horing, Andreas; Peternell, Thomas
  作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); University of Bayreuth
  摘要：Given a reflexive sheaf on a mildly singular projective variety, we prove a flatness criterion under certain stability conditions. This implies the algebraicity of leaves for sufficiently stable foliations with numerically trivial canonical bundle such that the second Chern class does not vanish. Combined with the recent works of Druel and Greb-Guenancia-Kebekus this establishes the Beauville-Bogomolov decomposition for minimal models with trivial canonical class.