Entropy and generic mean curvature flow in curved ambient spaces
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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.References
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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
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2663-2677
- MSC (2010): Primary 53C44; Secondary 53A35
- DOI: https://doi.org/10.1090/proc/13964
- MathSciNet review: 3778166