Stationary sets of the mean curvature flow with a forcing term
Julin, V., & Niinikoski, J. (2021). Stationary sets of the mean curvature flow with a forcing term. Advances in Calculus of Variations, Ahead of Print. https://doi.org/10.1515/acv-2021-0019
Published inAdvances in Calculus of Variations
DisciplineMatematiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköMathematicsAnalysis and Dynamics Research (Centre of Excellence)
© 2021 Walter de Gruyter GmbH
We consider the flat flow solution to the mean curvature equation with forcing in ℝn. Our main resultstates that tangential balls in ℝn 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 ofthe 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 ℝn for a constant forcing term as finite unions of equisize balls with mutually positive distance.
PublisherWalter de Gruyter GmbH
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