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.

Rectifiability of Varifolds with Locally Bounded First Variation with Respect to Anisotropic Surface Energies / De Philippis, G.; De Rosa, A.; Ghiraldin, F.. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 71:6(2018), pp. 1123-1148. [10.1002/cpa.21713]

Rectifiability of Varifolds with Locally Bounded First Variation with Respect to Anisotropic Surface Energies

De Philippis, G.;
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.
71
6
1123
1148
https://doi.org/10.1002/cpa.21713
https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.21713
https://arxiv.org/abs/1609.01908
De Philippis, G.; De Rosa, A.; Ghiraldin, F.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/85684
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