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A direct approach to Plateau's problem


De Lellis, Camillo; Ghiraldin, Francesco; Maggi, Francesco (2017). A direct approach to Plateau's problem. Journal of the European Mathematical Society, 19(8):2219-2240.

Abstract

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. © European Mathematical Society 2017.

Abstract

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. © European Mathematical Society 2017.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:27 June 2017
Deposited On:07 Nov 2017 15:11
Last Modified:19 Feb 2018 09:10
Publisher:European Mathematical Society
ISSN:1435-9855
OA Status:Green
Publisher DOI:https://doi.org/10.4171/JEMS/716

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