@article{63b587d2255d41108692a15e41138273,

title = "Rectifiability of Varifolds with Locally Bounded First Variation with Respect to Anisotropic Surface Energies",

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 1, this condition is shown to be equivalent to the strict convexity of the integrand with respect to the tangent plane.",

author = "{De Philippis}, Guido and {De Rosa}, Antonio and Francesco Ghiraldin",

note = "Funding Information: implying that condition (II) in Theorem B.1 is also satisfied. Hence is d -rectifiable. In particular, for -a.e. x, Tan.x; / D f!d1H d .TxK \ B/g. Since, by assumption, is invariant along the directions of Tx, this implies that Tx D TxK and concludes the proof. □ Acknowledgments. G.D.P. is supported by the MIUR SIR Grant “Geometric variational problems” (RBSI14RVEZ). A.D.R. is supported by SNF 159403, “Regularity questions in geometric measure theory.” The authors would like to thank U. Menne for some very accurate comments on a preliminary version of the paper that allowed us to improve the main result. Publisher Copyright: {\textcopyright} 2017 Wiley Periodicals, Inc.",

year = "2018",

month = jun,

doi = "10.1002/cpa.21713",

language = "English (US)",

volume = "71",

pages = "1123--1148",

journal = "Communications on Pure and Applied Mathematics",

issn = "0010-3640",

publisher = "Wiley-Liss Inc.",

number = "6",

}