#### 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 ${ℝ}^{k+1}$.

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##### Keywords
mean curvature flow, entropy, shrinker
Primary: 53C44
Secondary: 49Q20