English

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