Rigidity of self-shrinkers and translating solitons of mean curvature flows

被引：64

作者：

Chen, Qun ^{[1
]}

Qiu, Hongbing ^{[1
,2
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[2] Man Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany

来源：

ADVANCES IN MATHEMATICS | 2016年 / 294卷

关键词：

Self-shrinker; Translating soliton; Rigidity; Omori-Yau maximum principle; V-harmonic map; MAXIMUM PRINCIPLE; HARMONIC MAPS; GEOMETRIC APPLICATIONS; MINKOWSKI SPACE; HYPERSURFACES; MANIFOLDS;

D O I：

10.1016/j.aim.2016.03.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove that any complete m-dimensional spacelike self-shrinkers in pseudo-Euclidean spaces R-n(m+n) must be affine planes, and there exists no complete m-dimensional spacelike translating soliton in R-n(m+n). These results are proved by using a new Omori-Yau maximal principle. We also derive a rigidity theorem of self-shrinking hypersurfaces in Euclidean space with Gauss image lies in a regular ball. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：517 / 531

页数：15

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