A direct approach to Plateau's problem

  • Camillo De Lellis

    Universität Zürich, Switzerland
  • Francesco Ghiraldin

    Universität Zürich, Switzerland
  • Francesco Maggi

    University of Texas at Austin, USA


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.

Cite this article

Camillo De Lellis, Francesco Ghiraldin, Francesco Maggi, A direct approach to Plateau's problem. J. Eur. Math. Soc. 19 (2017), no. 8, pp. 2219–2240

DOI 10.4171/JEMS/716