Calculus of Variations and Geometric Measure Theory
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A. Chambolle - M. Novaga

Anisotropic and crystalline mean curvature flow of mean-convex sets

created by novaga on 25 Mar 2020
modified on 22 Jan 2021


Accepted Paper

Inserted: 25 mar 2020
Last Updated: 22 jan 2021

Journal: Ann. Scuola Normale Sup. Pisa
Year: 2020

ArXiv: 2004.00270 PDF


We consider a variational scheme for the anisotropic (including crystalline) mean curvature flow of sets with strictly positive anisotropic mean curvature. We show that such condition is preserved by the scheme, and we prove the strict convergence in $BV$ of the time-integrated perimeters of the approximating evolutions, extending a recent result of De Philippis and Laux to the anisotropic setting. We also prove uniqueness of the flat flow obtained in the limit.


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