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

Let M 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 k+1.

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mean curvature flow, entropy, shrinker
Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 49Q20
Received: 7 March 2018
Accepted: 29 September 2018
Published: 28 May 2019
Proposed: Tobias H Colding
Seconded: Gang Tian, Bruce Kleiner
Or Hershkovits
Department of Mathematics
Stanford University
Stanford, CA
United States
Brian White
Department of Mathematics
Stanford University
Stanford, CA
United States