A note on the entropy of mean curvature flow
Differential Geometry
2016-01-20 v2
Abstract
The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers and scales, and is invariant under rigid motions and dilations. As a consequence of Huisken's monotonicity formula, entropy is non-increasing under mean curvature flow. We show here that a compact mean convex hypersurface with some low entropy is diffeomorphic to a round sphere. We will also prove that a smooth self-shrinker with low entropy is exact a hyperplane.
Keywords
Cite
@article{arxiv.1409.1641,
title = {A note on the entropy of mean curvature flow},
author = {Chao Bao},
journal= {arXiv preprint arXiv:1409.1641},
year = {2016}
}
Comments
Accepted for publication in SCIENCE CHINA Mathematics