Relative expander entropy in the presence of a two-sided obstacle and applications
Differential Geometry
2020-04-01 v2 Analysis of PDEs
Abstract
We study a notion of relative entropy motivated by self-expanders of mean curvature flow. In particular, we obtain the existence of this quantity for arbitrary hypersurfaces trapped between two disjoint self-expanders asymptotic to the same cone. This allows us to begin to develop the variational theory for the relative entropy functional for the associated obstacle problem. We also obtain a version of the forward monotonicity formula for mean curvature flow proposed by Ilmanen.
Keywords
Cite
@article{arxiv.1906.07863,
title = {Relative expander entropy in the presence of a two-sided obstacle and applications},
author = {Jacob Bernstein and Lu Wang},
journal= {arXiv preprint arXiv:1906.07863},
year = {2020}
}
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34 pages, 0 figures