Annals of Mathematics

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• A stable trace formula III. Proof of the main theorems AI翻译
  作者：Arthur, J
• Convex integration for Lipschitz mappings and counterexamples to regularity AI翻译
  作者：Müller, S; Sverák, V
• On De Giorgi's conjecture in dimensions 4 and 5 AI翻译
  作者：Ghoussoub, N; Gui, CF
• Poles of Artin L-functions and the strong Artin conjecture AI翻译
  作者：Booker, AR
  摘要：We show that if the L-function of an irreducible 2-dimensional complex Galois representation over Q is not automorphic then it has infinitely many poles. In particular, the Artin conjecture for a single representation implies the corresponding strong Artin conjecture.
• A C1-generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources AI翻译
  作者：Bonatti, C; Díaz, LJ; Pujals, ER
  摘要：We show that, for every compact n-dimensional manifold, n greater than or equal to 1, there is a residual subset of Diff(1)(M) of diffeomorphisms for which the homoclinic class of any periodic saddle of f verifies one of the following two possibilities: Either it is contained in the closure of an infinite set of sinks or sources (Newhouse phenomenon), or it presents some weak form of hyperbolicity called dominated splitting (this is a generalization of a bidimensional result of Mane [Ma3]). In...
• Hochschild cohomology of factors with property Γ AI翻译
  作者：Christensen, E; Pop, F; Sinclair, AM; Smith, RR
  摘要：The main result of this paper is that the k(th) continuous Hochschild cohomology groups H-k(M,M) and Hk(M,B(H)) of a von Neumann factor M subset of or equal to B(H) of type II1 with property Gamma are zero for all positive integers k. The method of proof involves the construction of hyperfinite subfactors with special properties and a new inequality of Grothendieck type for multilinear maps. We prove joint continuity in the parallel to . parallel to(2)-norm of separately ultraweakly continuous...
• Poincare inequalities in punctured domains AI翻译
  作者：Lieb, EH; Seiringer, R; Yngvason, J
  摘要：The classic Poincare inequality bounds the L-q-norm of a function f in a bounded domain Omega subset of R-n in terms of some L-P-norm of its gradient in Omega. We generalize this in two ways: In the first generalization we remove a set Gamma from Omega and concentrate our attention on Lambda = Omega \ Gamma. This new domain might not even be connected and hence no Poincare inequality can generally hold for it, or if it does hold it might have a very bad constant. This is so even if the volume ...
• Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order AI翻译
  作者：Daubechies, I; DeVore, R
• Pair correlation densities of inhomogeneous quadratic forms AI翻译
  作者：Marklof, J
  摘要：Under explicit diophantine conditions on (alpha,beta) epsilon R-2, we prove that the local two-point correlations of the sequence given by the values (m - alpha)(2) + (n - beta)(2), with (m, n) epsilon Z(2), are those of a Poisson process. This partly confirms a conjecture of Berry and Tabor [2] on spectral statistics of quantized integrable systems, and also establishes a particular case of the quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms of signature (2,...
• Fundamental groups of manifolds with positive isotropic curvature AI翻译
  作者：Fraser, AM
  摘要：A central theme in Riemannian geometry is understanding the relationships between the curvature and the topology of a Riemannian manifold. Positive isotropic curvature (PIC) is a natural and much studied curvature condition which includes manifolds with pointwise quarter-pinched sectional curvatures and manifolds with positive curvature operator. By the results of Micallef and Moore there is only one topological type of compact simply connected manifold with PIC: namely any such manifold must ...