Sharp entropy bounds for self-shrinkers in mean curvature flow

Hershkovits, Or; White, Brian

doi:10.2140/gt.2019.23.1611

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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

DOI: 10.2140/gt.2019.23.1611

Abstract

Let $M \subset ℝ^{m + 1}$ be a smooth, closed, codimension-one self-shrinker (for mean curvature flow) with nontrivial $k^{th}$ 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

Mathematical Subject Classification 2010

Primary: 53C44

Secondary: 49Q20

References

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

Volume 23, issue 3 (2019)