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1940 The existence of minimal surfaces of given topological structure under prescribed boundary conditions
R. Courant
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Acta Math. 72: 51-98 (1940). DOI: 10.1007/BF02546328

Abstract

The purpose of the present paper is the solution of the boundary value problems for minimal surfaces when the boundaries are not, or not entirely-fixed Jordan curves but are free to move on prescribed manifolds. At the same time I shall present modifications and simplifications of my previous solution of the Plateau' and Douglas' problem for fixed boundary curves and prescribed topological structure and incidentally discuss certain features of the problem in order to clarify its relation to the theory of conformal mapping. Though based on previous publications, the paper may, except for some references, be read independently.

Note

Nos. [9], [10], [11], [12], [13], [14] of the bibliography at the end of the paper. References to this list are made in square brackets throughout this paper.

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R. Courant. "The existence of minimal surfaces of given topological structure under prescribed boundary conditions." Acta Math. 72 51 - 98, 1940. https://doi.org/10.1007/BF02546328

Information

Published: 1940
First available in Project Euclid: 31 January 2017

zbMATH: 66.0485.02
MathSciNet: MR2478
Digital Object Identifier: 10.1007/BF02546328

Rights: 1940 © Almqvist & Wiksells Boktryckeri-A.-B.

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