#### Volume 23, issue 3 (2019)

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Sharp entropy bounds for self-shrinkers in mean curvature flow

### Or Hershkovits and Brian White

Geometry & Topology 23 (2019) 1611–1619
##### Abstract

Let $M\subset {ℝ}^{m+1}$ be a smooth, closed, codimension-one self-shrinker (for mean curvature flow) with nontrivial homology. We show that the entropy of $M$ is greater than or equal to the entropy of a round $k$-sphere, and that if equality holds, then $M$ is a round $k$-sphere in ${ℝ}^{k+1}$.

##### Keywords
mean curvature flow, entropy, shrinker
Primary: 53C44
Secondary: 49Q20
##### Publication
Received: 7 March 2018
Accepted: 29 September 2018
Published: 28 May 2019
Proposed: Tobias H Colding
Seconded: Gang Tian, Bruce Kleiner
##### Authors
 Or Hershkovits Department of Mathematics Stanford University Stanford, CA United States Brian White Department of Mathematics Stanford University Stanford, CA United States