A direct approach to the anisotropic Plateau problem
  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 [DGM14, DPDRG15]. In particular, we perform a new strategy for proving the rectifiability of the minimal set, avoiding the Preiss' Rectifiability Theorem [Pre87]. 
Camillo De Lellis, Antonio De Rosa, Francesco Ghiraldin
math.AP