Evolution of hypersurfaces by the mean curvature minus an external force field

作     者：Yan-nan LIU Huai-yu JIAN 

作者机构：Department of Mathematical SciencesTsinghua UniversityBeijing 100084China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2007年第50卷第2期

页      面：231-239页

核心收录：

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

基　　金：This work was partially supported by the National Natural Science Foundation of China (Grant No. 10631020) Basic Research Grant of Tsinghua University (Grant No. JCJC2005071) 

主　　题：parabolic equation mean curvature flow maximum principle (for tensor) 35K45 53A05 

摘      要：In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is larger than some constant depending on the boundness of derivatives of the external force field. For a linear force, we prove that the convexity of the hypersurface is preserved during the evolution and the flow has a unique smooth solution in any finite time and expands to infinity as the time tends to infinity if the initial curvature is smaller than the slope of the force.