Document Zbl 0635.53033

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Tromba, Anthony J.

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.

MSC:

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

Keywords:

Douglas’ theorem; Plateau problem; Dirichlet functional

Citations:

Zbl 0635.53001

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