Premium
Rectifiability of Varifolds with Locally Bounded First Variation with Respect to Anisotropic Surface Energies
Author(s) -
De Philippis Guido,
De Rosa Antonio,
Ghiraldin Francesco
Publication year - 2018
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21713
Subject(s) - mathematics , bounded function , convexity , first variation , mathematical analysis , tangent , bounded variation , tangent space , codimension , bounded deformation , plane (geometry) , surface (topology) , pure mathematics , geometry , uniform boundedness , financial economics , economics
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 1, this condition is shown to be equivalent to the strict convexity of the integrand with respect to the tangent plane.© 2017 Wiley Periodicals, Inc.