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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
61/2016

Rectifiability of varifolds with locally bounded first variation with respect to anisotropic surface energies

Guido De Philippis, Antonio De Rosa and Francesco Ghiraldin

Abstract

In this paper we extend Allard's celebrated rectifiability theorem to the setting of varifolds with locally bounded first variation with respect to an anisotropic integrand. In particular, we identify a necessary and sufficient condition on the integrand to obtain the rectifiability of every $d$-dimensional varifold with locally bounded first variation and positive $d$-dimensional density. In codimension one, this condition is shown to be equivalent to the strict convexity of the integrand with respect to the tangent plane.

Received:
Sep 11, 2016
Published:
Sep 19, 2016
MSC Codes:
49Q15, 49Q20, 35J60
Keywords:
varifolds, First variation, rectifiability, Anisotropic

Related publications

inJournal
2018 Repository Open Access
Guido De Philippis, Antonio De Rosa and Francesco Ghiraldin

Rectifiability of varifolds with locally bounded first variation with respect to anisotropic surface energies

In: Communications on pure and applied mathematics, 71 (2018) 6, pp. 1123-1148