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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.
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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...
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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.
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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.
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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...
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作者：Guralnick, Robert M.; Tiep, Pham Huu
作者单位：State University System of Florida; University of Florida; University of Southern California
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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.
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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
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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.
