Inventiones mathematicae

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• On the capacity of surfaces in manifolds with nonnegative scalar curvature AI翻译
  作者：Bray, Hubert; Miao, Pengzi
  作者单位：Duke University; Monash University
  摘要：Given a surface in an asymptotically flat 3-manifold with nonnegative scalar curvature, we derive an upper bound for the capacity of the surface in terms of the area of the surface and the Willmore functional of the surface. The capacity of a surface is defined to be the energy of the harmonic function which equals 0 on the surface and goes to 1 at infinity. Even in the special case of R-3, this is a new estimate. More generally, equality holds precisely for a spherically symmetric sphere in a...
• On the spectral gap for finitely-generated subgroups of SU(2) AI翻译
  作者：Bourgain, Jean; Gamburd, Alex
  作者单位：Institute for Advanced Study - USA; University of California System; University of California Santa Cruz; University of California System; University of California Santa Cruz
  摘要：We prove the spectral gap property for free subgroups of SU(2) generated by elements satisfying a noncommutative diophantine property, in particular for free subgroups generated by elements with algebraic entries.
• Random data Cauchy theory for supercritical wave equations II: a global existence result AI翻译
  作者：Burq, Nicolas; Tzvetkov, Nikolay
  作者单位：Universite Paris Saclay; Institut Universitaire de France; Universite de Lille
  摘要：We prove that the subquartic wave equation on the three dimensional ball Theta, with Dirichlet boundary conditions admits global strong solutions for a large set of random supercritical initial data in boolean AND(s<1/2)(H-s(Theta) x Hs-1(Theta)). We obtain this result as a consequence of a general random data Cauchy theory for supercritical wave equations developed in our previous work [6] and invariant measure considerations, inspired by earlier works by Bourgain [2,3] on the non linear Schr...
• On local behavior of holomorphic functions along complex submanifolds of CN supercript stop AI翻译
  作者：Brudnyi, Alexander
  作者单位：University of Calgary
  摘要：In this paper we establish some general results on local behavior of holomorphic functions along complex submanifolds of C-N. As a corollary, we present multi-dimensional generalizations of an important result of Coman and Poletsky on Bernstein type inequalities on transcendental curves in C-2.
• Exotic smooth structures on small 4-manifolds AI翻译
  作者：Akhmedov, Anar; Park, B. Doug
  作者单位：University System of Georgia; Georgia Institute of Technology; University of Waterloo
  摘要：Let M be either CP2#3 (CP) over bar (2) or 3CP(2)#5 (CP) over bar (2). We construct the first example of a simply-connected irreducible symplectic 4-manifold that is homeomorphic but not diffeomorphic to M.
• Large time existence for 3D water-waves and asymptotics AI翻译
  作者：Alvarez-Samaniego, Borys; Lannes, David
  作者单位：Universite de Bordeaux; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：We rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre approximation and full-dispersion model. We first introduce a variable nondimensionalized version of the water-waves equations which vary from shallow to deep water, and which involves four dimensionless parameters. Using a nonlocal energy adapted to the equations, we can prove a wel...
• Symmetric powers and a problem of Kollar and Larsen AI翻译
  作者：Guralnick, Robert M.; Tiep, Pham Huu
  作者单位：State University System of Florida; University of Florida; University of Southern California
• Approximately invariant manifolds and global dynamics of spike states AI翻译
  作者：Bates, Peter W.; Lu, Kening; Zeng, Chongchun
  作者单位：Michigan State University; Brigham Young University; University System of Georgia; Georgia Institute of Technology
  摘要：We investigate the existence of a true invariant manifold given an approximately invariant manifold for an infinite-dimensional dynamical system. We prove that if the given manifold is approximately invariant and approximately normally hyperbolic, then the dynamical system has a true invariant manifold nearby. We apply this result to reveal the global dynamics of boundary spike states for the generalized Allen-Cahn equation.
• Cohomological characterizations of projective spaces and hyperquadrics AI翻译
  作者：Araujo, Carolina; Druel, Stephane; Kovacs, Sandor J.
  作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of Washington; University of Washington Seattle
• Displays and formal p-divisible groups AI翻译
  作者：Lau, Eike
  作者单位：University of Bielefeld
  摘要：Over p-adic Nagata rings, formal p-divisible groups are classified by nilpotent displays according to T. Zink. We extend this result to arbitrary p-adic rings. The proof uses the Grothendieck-Illusie deformation theory of truncated p-divisible groups.