# 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}
}
• Published 28 January 2015
• Mathematics
• arXiv: Analysis of PDEs
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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