Volume 22, issue 2 (2018)

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Topology of closed hypersurfaces of small entropy

Jacob Bernstein and Lu Wang

Geometry & Topology 22 (2018) 1109–1141
Abstract

We use a weak mean curvature flow together with a surgery procedure to show that all closed hypersurfaces in 4 with entropy less than or equal to that of S2 × , the round cylinder in 4, are diffeomorphic to S3.

Keywords
mean curvature flow, surgery, entropy, self-shrinker
Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 35K55, 57R65
References
Publication
Received: 28 June 2016
Revised: 3 February 2017
Accepted: 16 April 2017
Published: 16 January 2018
Proposed: Bruce Kleiner
Seconded: Tobias H. Colding, John Lott
Authors
Jacob Bernstein
Department Of Mathematics
Johns Hopkins University
Baltimore, MD
United States
Lu Wang
Department of Mathematics
University of Wisconsin
Madison, WI
United States