Annals of Mathematics

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• An infinite Ramsey theorem and some Banach-space dichotomies AI翻译
  作者：Gowers, WT
  摘要：A problem of Banach asks whether every infinite-dimensional Banach space which is isomorphic to all its infinite-dimensional subspaces must be isomorphic to a separable Hilbert space. In this paper we prove a result of a Ramsey-theoretic nature which implies an interesting dichotomy for subspaces of Banach spaces. Combined with a result of Komorowski and Tomczak-Jaegermann, this gives a positive answer to Banach's problem. We then generalize the Ramsey-theoretic result and deduce a further dic...
• Appendix: On certain dyadic representations AI翻译
  作者：Bushnell, CJ; Henniart, G
• Isoperimetric functions of groups and computational complexity of the word problem AI翻译
  作者：Birget, JC; Ol'shanskii, AY; Rips, E; Sapir, MV
  摘要：We prove that the word problem of a finitely generated group G is in NP (solvable in polynomial time by a nondeterministic Turing machine) if and only if this group is a subgroup of a finitely presented group H with polynomial isoperimetric function. The embedding can be chosen in such a way that G has bounded distortion in H. This completes the work started in [6] and [25].
• The solution of the Kato problem for divergence form elliptic operators with Gaussian heat kernel bounds AI翻译
  作者：Hofmann, S; Lacey, M; McIntosh, A
  摘要：We solve the Kato problem for divergence form elliptic operators whose heat kernels satisfy a pointwise Gaussian upper bound. More precisely, given the Gaussian hypothesis. we establish that the domain of the square root of a complex uniformly elliptic operator L = -div(Adel) with bounded measurable coefficients in R-n is the Sobolev space H-1(R-n) in any dimension with the estimate parallel torootLfparallel to(2) - parallel todelfparallel to(2). We note, in particular, that for such operators...
• Isoperimetric and isodiametric functions of groups AI翻译
  作者：Sapir, MV; Birget, JC; Rips, E
  摘要：This is the first of two papers devoted to connections between asymptotic functions of groups and computational complexity. In particular, we show how to construct a finitely presented group with NP-complete word problem. One of the main results of this paper states that if a real number alpha greater than or equal to 4 is computable in time less than or equal to 2(2Cm) for some constant C > 0 then n(alpha) is equivalent (big O) to the Dehn function of a finitely presented group. The smallest ...
• Almost every real quadratic map is either regular or stochastic AI翻译
  作者：Lyubich, M
  摘要：In this paper we complete a program to study measurable dynamics in the real quadratic family. Our goal was to prove that almost any real quadratic map P-c : z --> x(2) + c, c is an element of [-2.1/4], has either an attracting cycle or an absolutely continuous invariant measure. The final step, completed here. is to prove that the set of infinitely renormalizable parametric values c is an element of [-2, 1/4] has zero Lebesgue measure. We derive this from a Renormalization Theorem which asser...
• An equation of Monge-Ampere type in conformal geometry, and four-manifolds of positive Ricci curvature AI翻译
  作者：Chang, SYA; Gursky, MJ; Yang, PC
  摘要：We formulate natural conformally invariant conditions on a 4-manifold for the existence of a metric whose Schouten tensor satisfies a quadratic inequality. This inequality implies that the eigen-values of the Ricci tensor are positively pinched.
• Entropy waves, the zig-zag graph product, and new constant-degree expanders AI翻译
  作者：Reingold, O; Vadhan, S; Wigderson, A
  摘要：The main contribution of this work is a new type of graph product, which we call the zig-zag product, Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large one, its degree from the small one, and its expansion properties from both! Iteration yields simple explicit constructions of constant-degree expanders of arbitrary size, starting from one constant-size expander. Crucial to our intuition (and simple analysis) of the properties o...
• Shadows and convexity of surfaces AI翻译
  作者：Ghomi, M
  摘要：We study the geometry and topology of immersed surfaces in Euclidean 3-space whose Gauss map satisfies a certain two-piece-property, and solve the-shadow problem formulated by H. Wente.
• Hodge structures on abelian varieties of type III AI翻译
  作者：Abdulali, S
  摘要：We show that the usual Hodge conjecture implies the general Hodge conjecture for certain abelian varieties of type III, and use this to deduce the general Hodge conjecture for all powers of certain 4-dimensional abelian varieties of type III. We also show the existence of a Hodge structure M such that M occurs in the cohomology of an abelian variety, but the Tate twist M(1) does not occur in the cohomology of any abelian variety, even though it is effective.