The extension and convergence of mean curvature flow in higher codimension

Abstract

In this paper, we investigate the convergence of the mean curvature flow of closed submanifolds in R n + q \mathbb {R}^{n+q} . We show that if the initial submanifold satisfies some suitable integral curvature conditions, then along the mean curvature flow it will shrink to a round point in finite time.