Pinching estimates and motion of hypersurfaces by curvature functions

被引：101

作者：

Andrews, Ben ^{[1
]}

机构：

[1] Australian Natl Univ, CMA, Canberra, ACT 0200, Australia

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2007年 / 608卷

基金：

澳大利亚研究理事会;

关键词：

D O I：

10.1515/CRELLE.2007.051

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Second derivative pinching estimates are proved for a class of parabolic equations, including motion of hypersurfaces by curvature functions such as quotients of elementary symmetric functions of curvature. The estimates imply convergence of convex hypersurfaces to spheres under these flows, improving earlier results of B. Chow and the author. The result is obtained via a detailed analysis of gradient terms in the equations satisfied by second derivatives.

引用

页码：17 / 33

页数：17

共 10 条

[1] CONTRACTION OF CONVEX HYPERSURFACES IN EUCLIDEAN-SPACE [J].