2期

最新文章

• Rationally isotropic quadratic spaces are locally isotropic AI翻译
  作者：Panin, Ivan
  作者单位：University of Bielefeld
  摘要：Let R be a regular local ring, K its field of fractions and (V,phi) a quadratic space over R. Assume that R contains a field of characteristic zero we show that if (V,phi)aS- (R) K is isotropic over K, then (V,phi) is isotropic over R. This solves the characteristic zero case of a question raised by J.-L. Colliot-Th,lSne in [3]. The proof is based on a variant of a moving lemma from [7]. A purity theorem for quadratic spaces is proved as well. It generalizes in the charactersitic zero case the...
• The stable free rank of symmetry of products of spheres AI翻译
  作者：Hanke, Bernhard
  作者单位：University of Munich
  摘要：A well known conjecture in the theory of transformation groups states that if p is a prime and (acurrency sign/p) (r) acts freely on a product of k spheres, then ra parts per thousand currency signk. We prove this assertion if p is large compared to the dimension of the product of spheres. The argument builds on tame homotopy theory for non-simply connected spaces.
• Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem AI翻译
  作者：Garofalo, Nicola; Petrosyan, Arshak
  作者单位：Purdue University System; Purdue University
  摘要：We construct two new one-parameter families of monotonicity formulas to study the free boundary points in the lower dimensional obstacle problem. The first one is a family of Weiss type formulas geared for points of any given homogeneity and the second one is a family of Monneau type formulas suited for the study of singular points. We show the uniqueness and continuous dependence of the blowups at singular points of given homogeneity. This allows to prove a structural theorem for the singular...
• A microscopic convexity principle for nonlinear partial differential equations AI翻译
  作者：Bian, Baojun; Guan, Pengfei
  作者单位：McGill University; Tongji University
  摘要：We study microscopic convexity property of fully nonlinear elliptic and parabolic partial differential equations. Under certain general structure condition, we establish that the rank of Hessian a double dagger (2) u is of constant rank for any convex solution u of equation F(a double dagger (2) u,a double dagger u,u,x)=0. The similar result is also proved for parabolic equations. Some of geometric applications are also discussed.