Annals of Mathematics

最新文章

• A geometric proof of the Berger Holonomy Theorem AI翻译
  作者：Olmos, C
  摘要：We give a geometric proof of the Berger Holonomy Theorem. The proof uses Euclidean submanifold geometry of orbits and gives a link between Riemannian holonomy groups and normal holonomy groups.
• The perimeter inequality under Steiner symmetrization: Cases of equality AI翻译
  作者：Chlebík, M; Cianchi, A; Fusco, N
  摘要：Steiner symmetrization is known not to increase perimeter of sets in R-n. The sets whose perimeter is preserved under this symmetrization are characterized in the present paper.
• Grobner geometry of Schubert polynomials AI翻译
  作者：Knutson, A; Miller, E
  摘要：Given a permutation w is an element of S-n, we consider a determinantal ideal I-w whose generators are certain minors in the generic n x n matrix (filled with independent variables). Using 'multidegrees' as simple algebraic substitutes for torus-equivariant cohomology classes on vector spaces, our main theorems describe, for each ideal I-w: variously graded multidegrees and Hilbert series in terms of ordinary and double Schubert and Grothendieck polynomials; a Grobner basis consisting of minor...
• Quadratic forms of signature (2,2) and eigenvalue spacings on rectangular 2-tori AI翻译
  作者：Eskin, A; Margulis, G; Mozes, S
• A proof of the Kepler conjecture AI翻译
  作者：Hales, TC
• Inverse spectral problems and closed exponential systems AI翻译
  作者：Horváth, M
  摘要：Consider the inverse eigenvalue problem of the Schrodinger operator defined on a finite interval. We give optimal and almost optimal conditions for a set of eigenvalues to determine the Schrodinger operator. These conditions are simple closedness properties of the exponential system corresponding to the known eigenvalues. The statements contain nearly all former results of this topic. We give also conditions for recovering the Weyl-Titchmarsh m-function from its values m(lambda(n)).
• Rough solutions of the Einstein-vacuum equations AI翻译
  作者：Klainerman, S; Rodnianski, I
  摘要：This is the first in a series of papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein-vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. Following [Kl-Ro] we develop new analytic methods based on Strichartz-type inequalities which result in a gain of half a derivative relative to the classical result. ...
• The Tits alternative for Out(Fn) II: A Kolchin type theorem AI翻译
  作者：Bestvina, M; Feighn, M; Handel, M
  摘要：This is the second of two papers in which we prove the Tits alternative for Out(F-n).
• The diameter of the isomorphism class of a Banach space AI翻译
  作者：Johnson, WB; Odell, E
  摘要：We prove that if X is a separable infinite dimensional Banach space then its isomorphism class has,infinite diameter with respect to the Banach-Mazur distance. One step in the proof is to show that if X is elastic then X contains an isomorph of c(0). We call X elastic if for some K < infinity for every Banach space Y which embeds into X, the space Y is K-isomorphic to a subspace of X. We also prove that if X is a separable Banach space such that for some K < infinity every isomorph of X is K-e...
• The Lyapunov exponents of generic volume-preserving and symplectic maps AI翻译
  作者：Bochi, J; Viana, M
  摘要：We show that the integrated Lyapunov exponents of C-1 volume-preserving diffeomorphisms are simultaneously continuous at a given diffeomorphism only if the corresponding Oseledets splitting is trivial (all Lyapunov exponents are equal to zero) or else dominated (uniform hyperbolicity in the projective bundle) almost everywhere. We deduce a sharp dichotomy for generic volume-preserving diffeomorphisms on any compact manifold: almost every orbit either is projectively hyperbolic or has all Lyapu...