A direct approach to Plateau's problem
  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. 
Camillo De Lellis, Francesco Ghiraldin, Francesco Maggi
math.AP math.MG math.OC