Stationary sets of the mean curvature flow with a forcing term

Author:

Julin Vesa1ORCID,Niinikoski Joonas1ORCID

Affiliation:

1. Department of Mathematics and Statistics , University of Jyvaskyla , Jyvaskyla , Finland

Abstract

Abstract We consider the flat flow solution to the mean curvature equation with forcing in n {\mathbb{R}^{n}} . Our main result states that tangential balls in n {\mathbb{R}^{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 {\mathbb{R}^{n}} for a constant forcing term as finite unions of equisize balls with mutually positive distance.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

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