SOME EXTENSIONS OF THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

被引：1

作者：

Wu, Jiayong ^{[1
]}

机构：

[1] Shanghai Maritime Univ, Dept Math, Shanghai 201306, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2013年 / 33卷 / 01期

关键词：

mean curvature flow; Riemannian submanifold; integral curvature; maximal existence time; 1ST SINGULAR TIME; SURFACES;

D O I：

10.1016/S0252-9602(12)60203-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a family of smooth immersions of closed hypersurfaces in a locally symmetric Riemannian manifold with bounded geometry, moving by mean curvature flow, we show that at the first finite singular time of mean curvature flow, certain subcritical quantities concerning the second fundamental form blow up. This result not only generalizes a result of Le-Sesum and Xu-Ye-Zhao, but also extends the latest work of Le in the Euclidean case.

引用

页码：171 / 186

页数：16

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