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Published June 2021 | Submitted
Journal Article Open

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

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.

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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Additional details

Created:
August 20, 2023
Modified:
October 23, 2023