# Existence and soap film regularity of solutions to Plateau’s problem

@article{Harrison2013ExistenceAS, title={Existence and soap film regularity of solutions to Plateau’s problem}, author={Jenny Harrison and Harrison Pugh}, journal={Advances in Calculus of Variations}, year={2013}, volume={9}, pages={357 - 394} }

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 usual homological definition of span is replaced with a novel algebraic-topological notion. In particular, our new definition offers a significant improvement over existing homological definitions in the case that the boundary has multiple connected components. Let M be a connected, oriented compact manifold… Expand

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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… Expand

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