3期

最新文章

• Families of canonically polarized varieties over surfaces AI翻译
  作者：Kebekus, Stefan; Kovacs, Sandor J.
  作者单位：University of Cologne; University of Washington; University of Washington Seattle
  摘要：Shafarevich's hyperbolicity conjecture asserts that a family of curves over a quasi-projective 1-dimensional base is isotrivial unless the logarithmic Kodaira dimension of the base is positive. More generally it has been conjectured by Viehweg that the base of a smooth family of canonically polarized varieties is of log general type if the family is of maximal variation. In this paper, we relate the variation of a family to the logarithmic Kodaira dimension of the base and give an affirmative ...
• Mixed Hodge polynomials of character varieties AI翻译
  作者：Hausel, Tamas; Rodriguez-Villegas, Fernando
  作者单位：University of Oxford
  摘要：We calculate the E-polynomials of certain twisted GL( n, C)character varieties Mn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie- type GL( n, Fq) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL( n, C)- character variety. The calculation also leads to several conjectures about the cohomolo...
• Renormalization and blow up for charge one equivariant critical wave maps AI翻译
  作者：Krieger, J.; Schlag, W.; Tataru, D.
  作者单位：Harvard University; University of Chicago; University of California System; University of California Berkeley
  摘要：We prove the existence of equivariant finite time blow-up solutions for the wave map problem from R2+ 1 -> S-2 of the form u( t, r) = Q(lambda( t) r) + R(t, r) where u is the polar angle on the sphere, Q(r) = 2 arctan r is the ground state harmonic map, lambda(t) = t(-1-nu), and R(t, r) is a radiative error with local energy going to zero as t -> 0. The number nu > 1/2 can be prescribed arbitrarily. This is accomplished by first renormalizing the blow-up profile, followed by a perturbative ana...
• Random data Cauchy theory for supercritical wave equations I: local theory 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 study the local existence of strong solutions for the cubic nonlinear wave equation with data in H-s(M), s < 1/2, where M is a three dimensional compact Riemannian manifold. This problem is supercritical and can be shown to be strongly ill-posed (in theHadamard sense). However, after a suitable randomization, we are able to construct local strong solution for a large set of initial data in H-s(M), where s >= 1/4 in the case of a boundary less manifold and s >= 8/21 in the case of a manifold...
• Large derivatives, backward contraction and invariant densities for interval maps AI翻译
  作者：Bruin, H.; Rivera-Letelier, J.; Shen, W.; van Strien, S.
  作者单位：University of Surrey; Universidad Catolica del Norte; Chinese Academy of Sciences; University of Science & Technology of China, CAS; University of Warwick
  摘要：In this paper, we study the dynamics of a smooth multimodal interval map f with non-flat critical points and all periodic points hyperbolic repelling. Assuming that vertical bar Df(n)(f(c))vertical bar -> infinity as n -> infinity holds for all critical points c, we show that f satisfies the so-called backward contracting property with an arbitrarily large constant, and that f has an invariant probability mu which is absolutely continuous with respect to Lebesgue measure and the density of mu ...
• Symplectic embeddings of polydisks AI翻译
  作者：Guth, Larry
  作者单位：Stanford University
  摘要：If P and P' are symplectic polydisks of radii R-1 <= ... <= R-n and R-1' <= ... <= R-n', respectively, then we prove that P symplectically embeds in P' provided that C(n)R-1 <= R-1' and C(n)R-1...R-n <= R-1'...R-n'. Up to a constant factor, these conditions are optimal.
• Big line bundles over arithmetic varieties AI翻译
  作者：Yuan, Xinyi
  作者单位：Columbia University
• Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability AI翻译
  作者：Apostolov, Vestislav; Calderbank, DavidM. J.; Gauduchon, Paul; Tonnesen-Friedman, Christina W.
  作者单位：University of Quebec; University of Quebec Montreal; Bulgarian Academy of Sciences; University of Bath; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Union College
  摘要：This paper concerns the existence and explicit construction of extremal Kahler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of Hamiltonian 2-forms (as introduced and studied in previous papers in the series) but this paper is largely independent of that theory. We obtain a characterization, on a large family of projective bundles, of the 'admissible' Kahler classes (i.e., those compatible with the ...
• 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...
• 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...