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Journal of the European Mathematical Society

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Volume 19, Issue 8, 2017, pp. 2219–2240
DOI: 10.4171/JEMS/716

Published online: 2017-06-27

A direct approach to Plateau's problem

Camillo De Lellis[1], Francesco Ghiraldin[2] and Francesco Maggi[3]

(1) Universität Zürich, Switzerland
(2) Universität Zürich, Switzerland
(3) University of Texas at Austin, USA

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 elementary comparison arguments. Exploiting some additional techniques in geometric measure theory, we can use this principle to give a different proof of a theorem by Harrison and Pugh and to answer a question raised by Guy David.

Keywords: Plateau's problem, minimal surfaces, area minimization, geometric measure theory

De Lellis Camillo, Ghiraldin Francesco, Maggi Francesco: A direct approach to Plateau's problem. J. Eur. Math. Soc. 19 (2017), 2219-2240. doi: 10.4171/JEMS/716