A direct approach to Plateau's problem

2014/08/18 by Camillo De Lellis, De Lellis, Camillo, Francesco Ghiraldin +3 · 3 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC) #math.AP #math.MG #math.OC

paper · pdf · doi:10.48550/arxiv.1408.4047

Updated abstract and bibliographical references

arxiv created 2014/09/04 · arxiv updated 2014/09/05

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.

Cited by

• Plateau's Problem via covering spaces
• Optimal regularity up to the boundary for Plateau-quasi-minimizers
• Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach

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