Asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces

Abstract

In this paper, we introduce a monotonicity formula for the mean curvature flow which is related to self-expanders. Then we use the monotonicity to study the asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces.

10 pages, a global version of functional is introduced, more applications are found