Integral formula of Minkowski type and new characterization of the Wulff shape

被引：37

作者：

He, Yi Jun ^{[1
,2
]}

Li, Hai Zhong ^{[3
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[2] Shanxi Univ, Sch Mathemat Sci, Taiyuan 030006, Peoples R China

[3] Tsinghua Univ, Dept Mathemat Sci, Beijing 100084, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2008年 / 24卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Wulff shape; F-Weingarten operator; anisotropic principal curvature; r-th anisotropic mean curvature; integral formula of Minkowski type;

D O I：

10.1007/s10114-007-7116-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a positive function F on S-n which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature M-r for hypersurfaces in Rn+1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in Rn+1. We give some new characterizations of the Wulff shape by the use of our integral formulas of Minkowski type, in case F = 1 which reduces to some well- known results.

引用

页码：697 / 704

页数：8

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