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 …

We provide a compactness principle which is applicable to different formulations of Plateau's
problem in codimension one and which is exclusively based on the theory of Radon …

We prove that m-dimensional Lipschitz graphs with anisotropic mean curvature bounded in
L p, p> m, are regular almost everywhere in every dimension and codimension. This …

We prove a compactness principle for the anisotropic formulation of the Plateau problem in
any codimension, in the same spirit of the previous works of the authors. In particular, we …

The regularity theory for the area functional (in geometric measure theory) Page 1 The regularity
theory for the area functional (in geometric measure theory) Camillo De Lellis Abstract The aim …

We prove that a Hausdorff limit of Griffith almost-minimizers remains a Griffith almost-
minimizer. For this purpose, we introduce a new approach to the uniform concentration …

We prove a compactness principle for the anisotropic formulation of the Plateau problem in
codimension one, along the same lines of previous works of the authors [,]. In particular, we …

Soap films at equilibrium are modeled, rather than as surfaces, as regions of small total
volume through the introduction of a capillarity problem with a homotopic spanning …

In this paper we prove that if (u, K) is an almost-minimizer of the Griffith functional and K is ε-
close to a plane in some ball B⊂ RN while separating the ball B in two big parts, then K is C …

Plateau's problem is to find a surface with minimal area spanning a given boundary. Our
paper presents a theorem for codimension one surfaces in ℝ n in which the usual …