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Journal Articles Annali della Scuola Normale Superiore di Pisa, Classe di Scienze Year : 2022

Anisotropic and crystalline mean curvature flow of mean-convex sets

Mouvement par courbure moyenne anisotrope ou cristalline d'ensembles à courbure moyenne positive.

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Abstract

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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Dates and versions

hal-02525796 , version 1 (31-03-2020)
hal-02525796 , version 2 (27-10-2020)

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Cite

Antonin Chambolle, Matteo Novaga. Anisotropic and crystalline mean curvature flow of mean-convex sets. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2022, 23 (2), pp.623-643. ⟨10.2422/2036-2145.202005_009⟩. ⟨hal-02525796v2⟩
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