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

被引：51
|
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.
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页码：517 / 531
页数：15
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