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

2016/09/07 by Guido De Philippis, De Philippis, Guido, Antonio De Rosa +4 · 6 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1609.01908

Abstract

We extend Allard's celebrated rectifiability theorem to the setting of\nvarifolds with locally bounded first variation with respect to an anisotropic\nintegrand. In particular, we identify a sufficient and necessary condition on\nthe integrand to obtain the rectifiability of every (d )-dimensional varifold\nwith locally bounded first variation and positive (d )-dimensional density. In\ncodimension one, this condition is shown to be equivalent to the strict\nconvexity of the integrand with respect to the tangent plane.\n

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