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Generic uniqueness of expanders with vanishing relative entropy
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Deruelle, Alix and Schulze, Felix (2020) Generic uniqueness of expanders with vanishing relative entropy. Mathematische Annalen, 377 (3-4). pp. 1095-1127. doi:10.1007/s00208-020-02004-6 ISSN 0025-5831.
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Official URL: http://dx.doi.org/10.1007/s00208-020-02004-6
Abstract
We define a relative entropy for two self-similarly expanding solutions to mean curvature flow of hypersurfaces, asymptotic to the same cone at infinity. Adapting work of White (Indiana Univ Math J 36(3):567–602, 1987) and using recent results of Bernstein (Asymptotic structure of almost eigenfunctions of drift laplacians on conical ends) and Bernstein-Wang (The space of asymptotically conical self-expanders of mean curvature flow), we show that expanders with vanishing relative entropy are unique in a generic sense. This also implies that generically locally entropy minimising expanders are unique.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Mathematische Annalen | ||||||||
Publisher: | Springer Verlag | ||||||||
ISSN: | 0025-5831 | ||||||||
Official Date: | August 2020 | ||||||||
Dates: |
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Volume: | 377 | ||||||||
Number: | 3-4 | ||||||||
Page Range: | pp. 1095-1127 | ||||||||
DOI: | 10.1007/s00208-020-02004-6 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Open Access Version: |
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