Entropy and generic mean curvature flow in curved ambient spaces

Abstract

In this article, we generalize some recent results of Colding and Minicozzi on generic singularities of mean curvature flow to curved ambient spaces. To do so, we make use of a weighted monotonicity formula to derive an "almost monotonicity" for the entropy upon embedding into R-l. We are also led to study the continuity of the entropy functional in certain cases.