摘要
We investigate the integral conditions to extend the mean curvature flow in a Riemannian manifold. We prove that the mean curvature flow solution with finite total mean curvature at a finite time interval [0,T) can be extended over time T. Moreover,we show that the condition is optimal in some sense.
We investigate the integral conditions to extend the mean curvature flow in a Riemannian manifold. We prove that the mean curvature flow solution with finite total mean curvature at a finite time interval [0, T） can be extended over time T. Moreover, we show that the condition is optimal in some sense.
基金
supported by National Natural Science Foundation of China (Grant Nos. 10771187, 11071211)
the Trans-Century Training Programme Foundation for Talents by the Ministry of Education of China
the Natural Science Foundation of Zhejiang Province (Grant No. 101037)
the China Postdoctoral Science Foundation (Grant No. 20090461379)
关键词
平均曲率流
黎曼流形
积分
时间间隔
mean curvature flow, Riemannian manifold, maximal existence, integral curvature
