A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

doi:10.1016/S0252-9602(10)60102-6

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1053-1064.doi: 10.1016/S0252-9602(10)60102-6

A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

陈旭忠, 沈一兵**

Department of Mathematics, Zhejiang University, Hangzhou 310027, China

收稿日期:2006-12-29 修回日期:2008-09-30 出版日期:2010-07-20 发布日期:2010-07-20
基金资助:
Project supported partially by the National Natural Science Foundation of China (10871171) and the Chinese-Hungarian Sci. and Tech. cooperation (for 2007-2009)

A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

CHEN Xu-Zhong, SHEN Yi-Bing**

Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Received:2006-12-29 Revised:2008-09-30 Online:2010-07-20 Published:2010-07-20
Supported by:
Project supported partially by the National Natural Science Foundation of China (10871171) and the Chinese-Hungarian Sci. and Tech. cooperation (for 2007-2009)

摘要/Abstract

摘要：

Under the hypothesis of mean curvature flows of hypersurfaces, we prove that the limit of the smooth rescaling of the singularity is weakly convex. It is a generalization of the result due to G.Huisken and C. Sinestrari in [5]. These a-priori bounds are satisfied for mean convex hypersurfaces in locally symmetric Riemannian manifolds with
nonnegative sectional curvature.

关键词: Mean curvature flow, singularity, hypersurface, weakly convexity

Abstract:

Key words: Mean curvature flow, singularity, hypersurface, weakly convexity

中图分类号:

53C44

陈旭忠, 沈一兵. A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS[J]. 数学物理学报(英文版), 2010, 30(4): 1053-1064.

CHEN Xu-Zhong, SHEN Yi-Bing. A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS[J]. Acta mathematica scientia,Series B, 2010, 30(4): 1053-1064.

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A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

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