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arXiv · 1609.01908

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

Guido De Philippis·Antonio De Rosa·Francesco Ghiraldin
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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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Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin. 2016-09-07. Rectifiability of varifolds with locally bounded first variation with respect to anisotropic surface energies. https://arxiv.org/abs/1609.01908

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