A proof of Douglas’ theorem on the existence of disc like minimal surfaces spanning Jordan contours on \(R^ n\). (English) Zbl 0635.53033

Théorie des variétés minimales et applications, Sémin. Palaiseau/France 1983/1984, Astérisque 154-155, 39-50 (1988).
Summary: [For the entire collection see Zbl 0635.53001.]
An historical account of the Plateau problem is given together with a complete proof by a direct and elementary method of the fact that any minimum of the Dirichlet functional is conformal.


53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
49Q05 Minimal surfaces and optimization


Zbl 0635.53001