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arXiv · 1409.1641

A note on the entropy of mean curvature flow

Chao Bao
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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.

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Chao Bao. 2014-09-05. A note on the entropy of mean curvature flow. https://doi.org/10.1007/s11425-015-5018-0

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