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

被引：0
|
作者：
Liu, Yannan [1 ]
机构：
[1] Beijing Technol & Business Univ, Dept Math, Beijing 100048, Peoples R China
来源：
FRONTIERS OF MATHEMATICS IN CHINA | 2012年 / 7卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Parabolic equation; mean curvature flow; maximum principle (for tensor); VORTEX; FLOW;
D O I：
10.1007/s11464-012-0218-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the evolution of hypersurfaces by powers of mean curvature minus an external force field. We prove that when the power is 2, the flow has a long-time smooth solution for all time under some conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the external force field, with its any order derivatives, is bounded, and the field is convex with its eigenvalues satisfying a pinch inequality.
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页码：717 / 723
页数：7
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