Rectifiability of varifolds with locally bounded first variation with respect to anisotropic surface energies
Guido De Philippis, Antonio De Rosa, and Francesco Ghiraldin
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Submission date: 11. Sep. 2016
published in: Communications on pure and applied mathematics, 71 (2018) 6, p. 1123-1148
DOI number (of the published article): 10.1002/cpa.21713
MSC-Numbers: 49Q15, 49Q20, 35J60
Keywords and phrases: varifolds, First variation, rectifiability, Anisotropic
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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.