Entropy and generic mean curvature flow in curved ambient spaces

Mramor, Alexander

doi:10.1090/proc/13964

Entropy and generic mean curvature flow in curved ambient spaces
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by Alexander Mramor PDF

Proc. Amer. Math. Soc. 146 (2018), 2663-2677 Request permission

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

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