Calculus of Variations and Geometric Measure Theory
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C. De Lellis - F. Ghiraldin - F. Maggi

A direct approach to Plateau's problem

created by maggi on 25 Aug 2014
modified by delellis on 24 May 2017


Accepted Paper

Inserted: 25 aug 2014
Last Updated: 24 may 2017

Journal: JEMS
Pages: 16
Year: 2014


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.


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