English

A direct approach to Plateau's problem

Analysis of PDEs 2014-09-05 v2 Metric Geometry Optimization and Control

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.

Keywords

Cite

@article{arxiv.1408.4047,
  title  = {A direct approach to Plateau's problem},
  author = {Camillo De Lellis and Francesco Ghiraldin and Francesco Maggi},
  journal= {arXiv preprint arXiv:1408.4047},
  year   = {2014}
}

Comments

Updated abstract and bibliographical references

R2 v1 2026-06-22T05:32:15.715Z