Anisotropic and crystalline mean curvature flow of mean-convex sets

• Autores: Antonin Chambolle, Matteo Novaga
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 23, Nº 2, 2022, págs. 623-643
• Idioma: inglés
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• Resumen

  • We consider a variational scheme for the anisotropic and 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.