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
收藏
页码：267 / 287
页数：21
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