Topology of closed hypersurfaces of small entropy

Bernstein, Jacob; Wang, Lu

doi:10.2140/gt.2018.22.1109

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Topology of closed hypersurfaces of small entropy

Jacob Bernstein and Lu Wang

Geometry & Topology 22 (2018) 1109–1141

DOI: 10.2140/gt.2018.22.1109

Abstract

We use a weak mean curvature flow together with a surgery procedure to show that all closed hypersurfaces in $ℝ^{4}$ with entropy less than or equal to that of $S^{2} \times ℝ$ , the round cylinder in $ℝ^{4}$ , are diffeomorphic to $S^{3}$ .

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

Volume 22, issue 2 (2018)