Complete bounded λ-hypersurfaces in the weighted volume-preserving mean curvature flow

被引：7

作者：

Zhu, Yecheng ^{[1
,2
]}

Fang, Yi ^{[2
]}

Chen, Qing ^{[1
]}

机构：

[1] Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China

[2] Anhui Univ Technol, Dept Appl Math, Maanshan 243002, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2018年 / 61卷 / 05期

基金：

中国国家自然科学基金;

关键词：

volume comparison theorem; topology; second fundamental form; 8-Bakry-Emery Ricci tensor; mean curvature flow; SINGULARITIES; TENSOR;

D O I：

10.1007/s11425-016-9020-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the complete bounded lambda-hypersurfaces in the weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded lambda-hypersurfaces with |A| a (c) 1/2 alpha and get some applications of the volume comparison theorem. Secondly, we consider the relation among lambda, extrinsic radius k, intrinsic diameter d, and dimension n of the complete lambda hypersurface, and we obtain some estimates for the intrinsic diameter and the extrinsic radius. At last, we get some topological properties of the bounded lambda-hypersurface with some natural and general restrictions.

引用

页码：929 / 942

页数：14

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