A direct approach to Plateau's problem in any codimension

@article{Philippis2015ADA,
  title={A direct approach to Plateau's problem in any codimension},
  author={Guido De Philippis and Antonio De Rosa and Francesco Ghiraldin},
  journal={arXiv: Analysis of PDEs},
  year={2015}
}
This paper aims to propose a direct approach to solve the Plateau's problem in codimension higher than one. The problem is formulated as the minimization of the Hausdorff measure among a family of $d$-rectifiable closed subsets of $\mathbb R^n$: following the previous work \cite{DelGhiMag} the existence result is obtained by a compactness principle valid under fairly general assumptions on the class of competitors. Such class is then specified to give meaning to boundary conditions. We also… Expand
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A direct approach to Plateau's problem
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 measures and elementaryExpand
Existence and soap film regularity of solutions to Plateau’s problem
Abstract 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 ${\mathbb{R}^{n}}$ in which the usualExpand
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