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.
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页码：929 / 942
页数：14
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