Mean Curvature Flow via Convex Functions on Grassmannian Manifolds

作     者：Yuanlong XIN Ling YANG 

作者机构：Institute of Mathematics Fudan University Shanghai 200433 China. Max Planck Institute for the Mathematics in Sciences Inselstr. 22-24 Leibzig 04103 Germany. 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2010年第31卷第3期

页      面：315-328页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Project supported by the National Natural Science Foundation of China and the Science Foundation of the Ministry of Education of China 

主　　题：Mean curvature flow Convex function Gauss map 

摘      要：Using the convex functions on Grassmannian manifolds, the authors obtain the interior estimates for the mean curvature flow of higher codimension. Confinable properties of Gauss images under the mean curvature flow have been obtained, which reveal that if the Gauss image of the initial submanifold is contained in a certain sublevel set of the v-function, then all the Gauss images of the submanifolds under the mean curvature flow are also contained in the same sublevel set of the v-function. Under such restrictions, curvature estimates in terms of v-function composed with the Gauss map can be carried out.