Annals of Mathematics

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• Index theorems for holomorphic self-maps AI翻译
  作者：Abate, M; Bracci, F; Tovena, F
• Branched polymers and dimensional reduction AI翻译
  作者：Brydges, DC; Imbrie, JZ
  摘要：We establish an exact relation between self-avoiding branched polymers in D + 2 continuum dimensions and the hard-core continuum gas at negative activity in D dimensions. We review conjectures and results on critical exponents for D + 2 = 2,3,4 and show that they are corollaries of our result. We explain the connection (first proposed by Parisi and Sourlas) between branched polymers in D + 2 dimensions and the Yang-Lee edge singularity in D dimensions.
• The Erdos-Szemereldi problem on sum set and product set AI翻译
  作者：Chang, MC
  摘要：The basic theme of this paper is the fact that if A is a finite set of integers, then the sum and product sets cannot both be small. A precise formulation of this fact is Conjecture 1 below due to Erdos-Szemeredi [E-S]. (see also [Ell, IT], and [K-T] for related aspects.) Only much weaker results or very special cases of this conjecture are presently known. One approach consists of assuming the sum set A + A small and then deriving that the product set AA is large (using Freiman's structure th...
• Automorphism groups of finite dimensional simple algebras AI翻译
  作者：Gordeev, NL; Popov, VL
  摘要：We show that if a field k contains sufficiently many elements (for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic k-group over K is k-isomorphic to Aut(A circle times(k) K), where A is a finite dimensional simple algebra over k.
• Convex hypersurfaces of prescribed curvature (vol 156, pg 655, 2002) AI翻译
  作者：Guan, B; Guan, PF
• Global existence and convergence for a higher order flow in conformal geometry AI翻译
  作者：Brendle, S
• Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations AI翻译
  作者：Dafermos, M
  摘要：This paper considers a trapped characteristic initial value problem for the spherically symmetric Einstein-Maxwell-scalar field equations. For an open set of initial data whose closure contains in particular Reissner-Nordstrom data, the future boundary of the maximal domain of development is found to be a light-like surface along which the curvature blows up, and yet the metric can be continuously extended beyond it. This result is related to the strong cosmic censorship conjecture of Roger Pe...
• New upper bounds on sphere packings I AI翻译
  作者：Cohn, H; Elkies, N
  摘要：We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best. bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.
• Deligne's conjecture on 1-motives AI翻译
  作者：Barbieri-Viale, L; Rosenschon, A; Saito, M
  摘要：We reformulate a conjecture of Deligne on 1-motives by using the integral weight filtration of Gillet and Soule on cohomology, and prove it. This implies the original conjecture up to isogeny. If the degree of cohomology is at most two, we can prove the conjecture for the Hodge realization without isogeny, and even for 1-motives with torsion.
• Homotopy hyperbolic 3-manifolds are hyperbolic AI翻译
  作者：Gabai, D; Meyerhoff, GR; Thurston, N