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The Volume preserving crystalline mean curvature flow of convex sets in RN

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dc.contributor.author Bellettinia, 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.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.issn 0021-7824
dc.identifier.uri http://hdl.handle.net/10230/36154
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.
dc.description.sponsorship V. Caselles acknowledges partial support by PNPGC project, reference MTM2006-14836.
dc.format.mimetype application/pdf
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.title The Volume preserving crystalline mean curvature flow of convex sets in RN
dc.type info:eu-repo/semantics/article
dc.identifier.doi https://doi.org/10.1016/j.matpur.2009.05.016
dc.subject.keyword Crystalline mean curvature
dc.subject.keyword Volume preserving ϕ-regular and flat flows
dc.subject.keyword Convex bodies
dc.rights.accessRights info:eu-repo/semantics/openAccess
dc.type.version info:eu-repo/semantics/acceptedVersion


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