Calculus of Variations and Geometric Measure Theory

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 17 Jul 2018


Published Paper

Inserted: 25 aug 2014
Last Updated: 17 jul 2018

Journal: JEMS
Volume: 19
Number: 8
Pages: 2219–2240
Year: 2017


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.