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Closed hypersurfaces of low entropy in R⁴ are isotopically trivial

Bernstein, Jacob and Wang, Lu (2022) Closed hypersurfaces of low entropy in R⁴ are isotopically trivial. Duke Mathematical Journal, 171 (7). ISSN 0012-7094. doi:10.1215/00127094-2022-0012.

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We show that any closed connected hypersurface in ℝ⁴ with entropy less than or equal to that of the round cylinder is smoothly isotopic to the standard three-sphere.

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Additional Information:© 2022 Duke University Press. Received: 21 September 2020; Revised: 3 June 2021; Published: 15 May 2022. First available in Project Euclid: 14 April 2022. The first author was partially supported by the National Science Foundation (NSF) grants DMS-1609340 and DMS-1904674 and the Institute for Advanced Study with funding provided by the Charles Simonyi Endowment. The second author was partially supported by NSF grants DMS-2018221 (formerly DMS-1811144) and DMS-2018220 (formerly DMS-1834824), the Wisconsin Alumni Research Foundation, a Vilas Early Career Investigator Award by the University of Wisconsin–Madison, and a von Neumann Fellowship by the Institute for Advanced Study with funding from the Zürich Insurance Company and NSF grant DMS-1638352.
Funding AgencyGrant Number
Institute for Advanced StudyUNSPECIFIED
Wisconsin Alumni Research FoundationUNSPECIFIED
University of Wisconsin-MadisonUNSPECIFIED
Zürich Insurance CompanyUNSPECIFIED
Subject Keywords:isotopy, Mean curvature flow, self-expander, self-shrinker
Issue or Number:7
Classification Code:2020 Mathematics Subject Classification. Primary 53C44; Secondary 53A10, 35J20, 35K93, 57Q37
Record Number:CaltechAUTHORS:20220808-886715000
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Official Citation:Jacob Bernstein. Lu Wang. "Closed hypersurfaces of low entropy in R⁴ are isotopically trivial." Duke Math. J. 171 (7) 1531 - 1558, 15 May 2022.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:116170
Deposited By: George Porter
Deposited On:11 Aug 2022 23:44
Last Modified:11 Aug 2022 23:44

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