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Stability of the ball under volume preserving fractional mean curvature flow

  • Annalisa Cesaroni ORCID logo and Matteo Novaga ORCID logo EMAIL logo

Abstract

We consider the volume constrained fractional mean curvature flow of a nearly spherical set and prove long time existence and asymptotic convergence to a ball. The result applies in particular to convex initial data under the assumption of global existence. Similarly, we show exponential convergence to a constant for the fractional mean curvature flow of a periodic graph.

MSC 2010: 35E10; 35R11; 35B40

Award Identifier / Grant number: 2017SXBSX4

Funding statement: The authors were supported by the PRIN Project 2019/24 “Variational methods for stationary and evolution problems with singularities and interfaces” funded by Ministero dell’Università e della Ricerca (2017SXBSX4).

  1. Communicated by: Yoshihiro Tonegawa

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Received: 2022-04-12
Revised: 2022-07-01
Accepted: 2022-07-07
Published Online: 2022-10-08
Published in Print: 2024-04-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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