Closed hypersurfaces of low entropy in R4 are isotopically trivial

Jacob Bernstein; Lu Wang

doi:10.1215/00127094-2022-0012

Abstract

We show that any closed connected hypersurface in ${\mathbb{R}^{4}}$ with entropy less than or equal to that of the round cylinder is smoothly isotopic to the standard three-sphere.

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Jacob Bernstein. Lu Wang. "Closed hypersurfaces of low entropy in ${\mathbb{R}^{4}}$ are isotopically trivial." Duke Math. J. 171 (7) 1531 - 1558, 15 May 2022. https://doi.org/10.1215/00127094-2022-0012

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Received: 21 September 2020; Revised: 3 June 2021; Published: 15 May 2022

First available in Project Euclid: 14 April 2022

MathSciNet: MR4484213

zbMATH: 1500.53093

Digital Object Identifier: 10.1215/00127094-2022-0012

Subjects:

Primary: 53C44

Secondary: 35J20 , 35K93 , 53A10 , 57Q37

Keywords: isotopy , Mean curvature flow , self-expander , self-shrinker

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