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Stationary sets of the mean curvature flow with a forcing term

  • Vesa Julin ORCID logo EMAIL logo and Joonas Niinikoski ORCID logo
Published/Copyright: August 8, 2021

Abstract

We consider the flat flow solution to the mean curvature equation with forcing in n . Our main result states that tangential balls in n under a flat flow with a bounded forcing term will experience fattening, which generalizes the result in [N. Fusco, V. Julin and M. Morini, Stationary sets and asymptotic behavior of the mean curvature flow with forcing in the plane, preprint 2020, https://arxiv.org/abs/2004.07734] from the planar case to higher dimensions. Then, as in the planar case, we characterize stationary sets in n for a constant forcing term as finite unions of equisize balls with mutually positive distance.

MSC 2010: 35K93; 35B38; 58E12

Communicated by Frank Duzaar


Funding source: Academy of Finland

Award Identifier / Grant number: 314227

Funding statement: The research was supported by the Academy of Finland grant 314227.

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Received: 2021-03-04
Revised: 2021-05-31
Accepted: 2021-06-04
Published Online: 2021-08-08
Published in Print: 2023-04-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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