A direct approach to Plateau's problem
By Camillo De Lellis, Francesco Ghiraldin, Francesco Maggi. 2014
59 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a60725b81b3a776fb47ead4aeb407bbc71672bd6
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In Applied Mathematics
Citations in the corpus
- Rectifiability of Varifolds with Locally Bounded First Variation with Respect to Anisotropic Surface Energies (2016, result): “Hence, if F satisfies (AC), this varifold is rectifiable and it can be shown that its support minimizes F; see the forthcoming papers [12, 15] and also [8, 9, 11] for similar results obtained with different techniques.”