Published Paper
Inserted: 7 sep 2016
Last Updated: 11 jan 2022
Journal: Comm. Pure App. Math.
Year: 2018
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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