Some Recent Progress on Mean Curvature Flow of Arbitrary Codimension

摘要

We give a survey on some results on the mean curvature flow of arbitrary codimension. Firstly, we present some sufficient conditions that assure the extension of the mean curvature flow over the time. Secondly, we discuss the convergence of mean curvature flow under integral or pointwise curvature pinching conditions. At last, we propose some unsolved problems that are related to our theorems.