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Entropy and generic mean curvature flow in curved ambient spaces


Author: Alexander Mramor
Journal: Proc. Amer. Math. Soc. 146 (2018), 2663-2677
MSC (2010): Primary 53C44; Secondary 53A35
DOI: https://doi.org/10.1090/proc/13964
Published electronically: February 16, 2018
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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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Additional Information

Alexander Mramor
Affiliation: Department of Mathematics, University of California Irvine, 340 Rowland Hall, Irvine, California 92697
Email: mramora@uci.edu

DOI: https://doi.org/10.1090/proc/13964
Received by editor(s): July 5, 2017
Received by editor(s) in revised form: September 10, 2017
Published electronically: February 16, 2018
Communicated by: Lei Ni
Article copyright: © Copyright 2018 American Mathematical Society

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