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...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.展开更多
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+1 种基金the Natural Science Foundation of Zhejiang Province (Grant No. 101037)the China Postdoctoral Science Foundation (Grant No. 20090461379)
文摘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.
