Entropy and generic mean curvature flow in curved ambient spaces

Abstract

In the 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 ${\mathbb{R}}^{\ell }$. We are also lead to study the continuity of the entropy functional in certain cases.

Fixed numerous typos and clarified some statements. Expanded discussion of main result. arXiv admin note: text overlap with arXiv:0908.3788 by other authors