Smooth compactness of self-shrinkers

被引：61

作者：

Colding, Tobias H. ^{[1
]}

Minicozzi, William P., II ^{[2
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

[2] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

来源：

COMMENTARII MATHEMATICI HELVETICI | 2012年 / 87卷 / 02期

基金：

美国国家科学基金会;

关键词：

Geometric flows; mean curvature flow; self-shrinker; singularities; EMBEDDED MINIMAL-SURFACES; MEAN-CURVATURE FLOW; FIXED GENUS; SPACE; SINGULARITIES; CONSTRUCTION; DISKS;

D O I：

10.4171/CMH/260

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a smooth compactness theorem for the space of embedded self-shrinkers in R-3. Since self-shrinkers model singularities in mean curvature flow, this theorem can be thought of as a compactness result for the space of all singularities and it plays an important role in studying generic mean curvature flow.

引用

页码：463 / 475

页数：13

共 31 条

[1] FIRST VARIATION OF A VARIFOLD [J].