A direct approach to the anisotropic Plateau problem

TL;DR

This paper establishes a compactness principle for the anisotropic Plateau problem in codimension one, introducing a new strategy to prove rectifiability of minimal sets without relying on Preiss' Rectifiability Theorem.

Contribution

It presents a novel approach to proving rectifiability in the anisotropic Plateau problem, simplifying previous methods and extending the theoretical framework.

Findings

Proved a compactness principle for anisotropic Plateau problem

Developed a new strategy for rectifiability proof

Avoided reliance on Preiss' Rectifiability Theorem

Abstract

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].