arXiv:1408.4047 Abstract | arXiv Analytics

arXiv:1408.4047 [math.AP]Abstract References Reviews Resources

A direct approach to Plateau's problem

Camillo De Lellis, Francesco Ghiraldin, Francesco Maggi

Published 2014-08-18, updated 2014-09-04Version 2

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.

Comments: Updated abstract and bibliographical references

Categories: math.AP, math.MG, math.OC

Keywords: plateaus problem, direct approach, elementary comparison arguments, radon measures

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