Annals of Mathematics

最新文章

• Grothendieck's problems concerning profinite completions and representations of groups AI翻译
  作者：Bridson, MR; Grunewald, FJ
  摘要：In 1970 Alexander Grothendieck [6] posed the following problem: let Gamma(1) and Gamma(2) be finitely presented, residually finite groups, and let u : Gamma(1) --> Gamma(2) be a homomorphism such that the induced map of profinite completions u : Gamma(1) --> Gamma(2) is an isomorphism; does it follow that u is an isomorphism? In this paper we settle this problem by exhibiting pairs of groups u : P --> Gamma such that Gamma is a direct product of two residually finite, hyperbolic groups, P is a...
• Higher composition laws III: The parametrization of quartic rings AI翻译
  作者：Bhargava, M
• On planar web geometry through abelian relations and connections AI翻译
  作者：Hénaut, A
• Real polynomial diffeomorphisms with maximal entropy: Tangencies AI翻译
  作者：Bedford, E; Smillie, J
• Quasiconformal homeomorphisms and the convex hull boundary AI翻译
  作者：Epstein, DBA; Marden, A; Markovic, V
  摘要：We investigate the relationship between an open simply-connected region Omega subset of S-2 and the boundary Y of the hyperbolic convex hull in H-3 of S-2 \ Omega. A counterexample is given to Thurston's conjecture that these spaces are related by a 2-quasiconformal homeomorphism which extends to the identity map on their common boundary, in the case when the homeomorphism is required to respect any group of Mobius transformations which preserves Q. We show that the best possible universal lip...
• An isoperimetric inequality for logarithmic capacity of polygons AI翻译
  作者：Solynin, AY; Zalgaller, VA
  摘要：We verify an old conjecture of G. Polya and G. Szego saying that the regular n-gon minimizes the logarithmic capacity among all n-gons with a fixed area.
• Classification of local conformal nets. Case c<1 AI翻译
  作者：Kawahigashi, Y; Longo, R
  摘要：We completely classify diffeomorphism covariant local nets of von Neumann algebras on the circle with central charge c less than 1. The irreducible ones are in bijective correspondence with the pairs of A-D-2n-E-6,E-8 Dynkin diagrams such that the difference of their Coxeter numbers is equal to 1. We first identify the nets generated by irreducible representations of the Virasoro algebra for c < 1 with certain coset nets. Then, by using the classification of modular invariants for the minimal ...
• Duality of metric entropy AI翻译
  作者：Artstein, S; Milman, V; Szarek, SJ
  摘要：For two convex bodies K and T in R-n, the covering number of K by T, denoted N(K, T), is defined as the minimal number of translates of T needed to cover K. Let us denote by K-o the polar body of K and by D the euclidean unit ball in R-n. We prove that the two functions of t, N(K, tD) and N(D, tK(o)), are equivalent in the appropriate sense, uniformly over symmetric convex bodies K subset of R-m and over n is an element of N. In particular, this verifies the duality conjecture for entropy numb...
• Metric attractors for smooth unimodal maps AI翻译
  作者：Graczyk, J; Sands, D; Swiatek, G
  摘要：We classify the measure theoretic attractors of general C-3 unimodal maps with quadratic critical points. The main ingredient is the decay of geometry.
• On the volume of the intersection of two Wiener sausages AI翻译
  作者：van den Berg, M; Bolthausen, E; den Hollander, F
  摘要：For a > 0, let W-1(a)(t) and W-2(a)(t) be the a-neighbourhoods of two independent standard Brownian motions in R-d starting at 0 and observed until time t. We prove that, for d greater than or equal to 3 and c > 0, lim (t-->infinity) log 1/t((d-2/d)) log P (\W-1(a)(ct) boolean AND W-2(a)(ct)\ greater than or equal to t) = -I-d(kappaa)(c) and derive a variational representation for the rate constant I-d(kappaa)(c). Here, kappa(a) is the Newtonian capacity of the ball with radius a. We show that...