We prove a local existence and uniqueness result of crystalline mean curvature flow starting from a compact convex admissible set in IRN. This theorem can handle the facet breaking/bending phenomena, and can be generalized to any anisotropic mean curvature flow. The method provides also a generalized geometric evolution starting from any compact convex set, existing up to the extinction time, satisfying a comparison principle, and defining a continuous semigroup in time. We prove that, when the initial set is convex, our evolution coincides with the flat phi-curvature flow in the sense of Almgren-Taylor-Wang. As a by-product, it turns out that the flat phi-curvature flow starting from a compact convex set is unique.

Bellettini, G., Caselles, V., Chambolle, A., Novaga, M. (2006). Crystalline mean curvature flow of convex sets. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 179(1), 109-152 [10.1007/s00205-005-0387-0].

Crystalline mean curvature flow of convex sets

BELLETTINI, GIOVANNI;
2006-01-01

Abstract

We prove a local existence and uniqueness result of crystalline mean curvature flow starting from a compact convex admissible set in IRN. This theorem can handle the facet breaking/bending phenomena, and can be generalized to any anisotropic mean curvature flow. The method provides also a generalized geometric evolution starting from any compact convex set, existing up to the extinction time, satisfying a comparison principle, and defining a continuous semigroup in time. We prove that, when the initial set is convex, our evolution coincides with the flat phi-curvature flow in the sense of Almgren-Taylor-Wang. As a by-product, it turns out that the flat phi-curvature flow starting from a compact convex set is unique.
2006
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
LEVEL SETS; MOTION; SINGULARITIES; SURFACES; PLANE; ALGORITHM; EVOLUTION; EQUATION; CURVES
Bellettini, G., Caselles, V., Chambolle, A., Novaga, M. (2006). Crystalline mean curvature flow of convex sets. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 179(1), 109-152 [10.1007/s00205-005-0387-0].
Bellettini, G; Caselles, V; Chambolle, A; Novaga, M
Articolo su rivista
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/37217
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 51
social impact