The Volume preserving crystalline mean curvature flow of convex sets in RN
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- dc.contributor.author Bellettini, Giovanni
- dc.contributor.author Caselles, Vicente
- dc.contributor.author Chambolle, Antonin
- dc.contributor.author Novaga, Matteo
- dc.date.accessioned 2018-12-19T16:35:57Z
- dc.date.available 2018-12-19T16:35:57Z
- dc.date.issued 2009
- dc.description.abstract We prove the existence of a volume preserving crystalline mean curvature flat flow starting from a compact convex set and its convergence, modulo a time-dependent translation, to a Wulff shape with the corresponding volume. We also prove that if C satisfies an interior ball condition (the ball being the Wulff shape), then the evolving convex set satisfies a similar condition for some time. To prove these results we establish existence, uniqueness and short-time regularity for the crystalline mean curvature flat flow with a bounded forcing term starting from C, showing in this case the convergence of an approximation algorithm due to Almgren, Taylor and Wang. Next we study the evolution of the volume and anisotropic perimeter, needed for the proof of the convergence to the Wulff shape as.en
- dc.description.sponsorship V. Caselles acknowledges partial support by PNPGC project, reference MTM2006-14836.
- dc.format.mimetype application/pdf
- dc.identifier.citation Bellettinia G, Caselles V, Chambolle A, Novaga M. The Volume preserving crystalline mean curvature flow of convex sets in RN. J Math Pures Appl. 2009 Nov;92(5):499-527. DOI: 10.1016/j.matpur.2009.05.016
- dc.identifier.doi http://dx.doi.org/10.1016/j.matpur.2009.05.016
- dc.identifier.issn 0021-7824
- dc.identifier.uri http://hdl.handle.net/10230/36154
- dc.language.iso eng
- dc.publisher Elsevier
- dc.relation.ispartof Journal de Mathématiques Pures et Appliquées. 2009 Nov;92(5):499-527
- dc.rights © Elsevier http://dx.doi.org/10.1016/j.matpur.2009.05.016
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.subject.keyword Crystalline mean curvature
- dc.subject.keyword Volume preserving ϕ-regular and flat flows
- dc.subject.keyword Convex bodies
- dc.title The Volume preserving crystalline mean curvature flow of convex sets in RN
- dc.type info:eu-repo/semantics/article
- dc.type.version info:eu-repo/semantics/acceptedVersion