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.
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| 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. | ||||||||||||||||
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| 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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