2-Dimensional complete self-shrinkers in R3

被引：24

作者：

Cheng, Qing-Ming ^{[1
]}

Ogata, Shiho ^{[2
]}

机构：

[1] Fukuoka Univ, Dept Appl Math, Fac Sci, Fukuoka 8140180, Japan

[2] Fukuoka Univ, Grad Sch Sci, Dept Appl Math, Fukuoka 8140180, Japan

来源：

MATHEMATISCHE ZEITSCHRIFT | 2016年 / 284卷 / 1-2期

关键词：

Mean curvature flow; Complete self-shrinkers; The generalized maximum principle; MEAN-CURVATURE FLOW; CURVE SHORTENING FLOW; RIGIDITY THEOREMS; SINGULARITIES;

D O I：

10.1007/s00209-016-1665-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is our purpose to study complete self-shrinkers in Euclidean space. By making use of the generalized maximum principle for -operator, we give a complete classification for 2-dimensional complete self-shrinkers with constant squared norm of the second fundamental form in . Ding and Xin (Trans Am Math Soc 366:5067-5085, 2014) have proved this result under the assumption of polynomial volume growth, which is removed in our theorem.

引用

页码：537 / 542

页数：6

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