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.
Funding source: Ministero dell’Università e della Ricerca
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).
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Communicated by: Yoshihiro Tonegawa
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