A mean value inequality for the generalized self-expander type submanifolds and its application

Abstract

In this paper we get a version of mean value inequality for generalized self-expander type submanifolds in Euclidean space. As the application, we prove that if mean curvature flow M(t) on the selfexpander in Euclidean space subconverges to an n-rectifiable varifold T in weak sense for t goes to the singular time, then T must be the cone.