Calculus of Variations and Geometric Measure Theory
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G. De Philippis - A. De Rosa - F. Ghiraldin

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

created by dephilipp on 07 Sep 2016
modified by derosa on 14 Nov 2016

[BibTeX]

Accepted Paper

Inserted: 7 sep 2016
Last Updated: 14 nov 2016

Journal: Comm. Pure App. Math.
Year: 2016

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 one, this condition is shown to be equivalent to the strict convexity of the integrand with respect to the tangent plane.


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