Geodesic
A direct approach to Plateau's problem
Journal of the European Mathematical Society, Tome 19 (2017) no. 8, pp. 2219-2240.

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/716
Classification : 49-XX
Keywords: Plateau's problem, minimal surfaces, area minimization, geometric measure theory 
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Camillo De Lellis; Francesco Ghiraldin; Francesco Maggi. A direct approach to Plateau's problem. Journal of the European Mathematical Society, Tome 19 (2017) no. 8, pp. 2219-2240. doi : 10.4171/jems/716. http://geodesic.mathdoc.fr/articles/10.4171/jems/716/

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