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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. https://resolver.caltech.edu/CaltechAUTHORS:20220808-886715000

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1215/00127094-2022-0012DOIArticle
https://arxiv.org/abs/2003.13858arXivDiscussion Paper
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.
Funders:
Funding AgencyGrant Number
NSFDMS-1609340
NSFDMS-1904674
Institute for Advanced StudyUNSPECIFIED
NSFDMS-2018221
NSFDMS-1811144
NSFDMS-2018220
NSFDMS-1834824
Wisconsin Alumni Research FoundationUNSPECIFIED
University of Wisconsin-MadisonUNSPECIFIED
Zürich Insurance CompanyUNSPECIFIED
NSFDMS-1638352
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
DOI:10.1215/00127094-2022-0012
Record Number:CaltechAUTHORS:20220808-886715000
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220808-886715000
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. https://doi.org/10.1215/00127094-2022-0012
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:116170
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:11 Aug 2022 23:44
Last Modified:11 Aug 2022 23:44

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