Volume-preserving mean curvature flow of hypersurfaces in space forms

被引：5

作者：

Xu, Hongwei ^{[1
]}

Leng, Yan ^{[1
]}

Zhao, Entao ^{[1
]}

机构：

[1] Zhejiang Univ, Ctr Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2014年 / 25卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Volume-preserving mean curvature flow; space forms; convergence theorem; integral curvature pinching; RELATING DIAMETER; EUCLIDEAN-SPACE; SPHERES; SUBMANIFOLDS; SURFACES; PLANE;

D O I：

10.1142/S0129167X14500219

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this paper is to investigate the convergence of the volume-preserving mean curvature flow of closed hypersurfaces in space forms. Assume that the initial hypersurface satisfies suitable integral curvature pinching conditions. We prove that along the volume-preserving mean curvature flow the initial hypersurface will be deformed to a totally umbilical sphere.

引用

页数：19

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