CONVEX ANCIENT SOLUTIONS OF THE MEAN CURVATURE FLOW

被引：0

作者：

Huisken, Gerhard ^{[1
]}

Sinestrari, Carlo ^{[2
]}

机构：

[1] Univ Tubingen, Fachbereich Math, D-72076 Tubingen, Germany

[2] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2015年 / 101卷 / 02期

关键词：

RICCI FLOW; HYPERSURFACES; SINGULARITIES; CLASSIFICATION;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study solutions of the mean curvature flow which are defined for all negative times, usually called ancient solutions. We give various conditions ensuring that a closed convex ancient solution is a shrinking sphere. Examples of such conditions are: a uniform pinching condition on the curvatures, a suitable growth bound on the diameter, or a reverse isoperimetric inequality. We also study the behaviour of uniformly k-convex solutions, and consider generalizations to ancient solutions immersed in a sphere.

引用

页码：267 / 287

页数：21

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