Rectifiability of Varifolds with Locally Bounded First Variation with Respect to Anisotropic Surface Energies

Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin

Research output: Contribution to journalArticle

Abstract

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 sufficient and necessary 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 1, this condition is shown to be equivalent to the strict convexity of the integrand with respect to the tangent plane.

Original languageEnglish (US)
Pages (from-to)1123-1148
Number of pages26
JournalCommunications on Pure and Applied Mathematics
Volume71
Issue number6
DOIs
StatePublished - Jun 2018

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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