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The space of asymptotically conical self-expanders of mean curvature flow

Bernstein, Jacob and Wang, Lu (2021) The space of asymptotically conical self-expanders of mean curvature flow. Mathematische Annalen, 380 (1-2). pp. 175-230. ISSN 0025-5831. doi:10.1007/s00208-021-02147-0. https://resolver.caltech.edu/CaltechAUTHORS:20210212-085010758

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Abstract

We show that the space of asymptotically conical self-expanders of the mean curvature flow is a smooth Banach manifold. An immediate consequence is that non-degenerate self-expanders—that is, those self-expanders that admit no non-trivial normal Jacobi fields that fix the asymptotic cone—are generic in a certain sense.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00208-021-02147-0DOIArticle
https://rdcu.be/cfa11PublisherFree ReadCube access
https://arxiv.org/abs/1712.04366arXivDiscussion Paper
ORCID:
AuthorORCID
Wang, Lu0000-0001-5263-3123
Additional Information:© The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021. Received 23 July 2018; Revised 28 July 2020; Accepted 08 January 2021; Published 19 January 2021. Lu Wang would like to thank David Hoffman, Bing Wang and Brian White for helpful discussions. Jacob Bernstein was partially supported by the NSF Grant DMS-1609340. Lu Wang was partially supported by the NSF Grants DMS-1811144 and DMS-1834824, an Alfred P. Sloan Research Fellowship, the office of the Vice Chancellor for Research and Graduate Education at the University of Wisconsin-Madison with funding from the Wisconsin Alumni Research Foundation and a Vilas Early Investigator Award. Communicated by F.C. Marques.
Funders:
Funding AgencyGrant Number
NSFDMS-1609340
NSFDMS-1811144
NSFDMS-1834824
Alfred P. Sloan FoundationUNSPECIFIED
University of Wisconsin-MadisonUNSPECIFIED
Wisconsin Alumni Research FoundationUNSPECIFIED
Vilas Early Investigator AwardUNSPECIFIED
Issue or Number:1-2
DOI:10.1007/s00208-021-02147-0
Record Number:CaltechAUTHORS:20210212-085010758
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210212-085010758
Official Citation:Bernstein, J., Wang, L. The space of asymptotically conical self-expanders of mean curvature flow. Math. Ann. 380, 175–230 (2021). https://doi.org/10.1007/s00208-021-02147-0
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108030
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Feb 2021 17:23
Last Modified:26 May 2021 22:16

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