- Acta Math.
- Volume 72 (1940), 51-98.
The existence of minimal surfaces of given topological structure under prescribed boundary conditions
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.
Nos. , , , , ,  of the bibliography at the end of the paper. References to this list are made in square brackets throughout this paper.
Acta Math., Volume 72 (1940), 51-98.
First available in Project Euclid: 31 January 2017
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1940 © Almqvist & Wiksells Boktryckeri-A.-B.
Courant, R. The existence of minimal surfaces of given topological structure under prescribed boundary conditions. Acta Math. 72 (1940), 51--98. doi:10.1007/BF02546328. https://projecteuclid.org/euclid.acta/1485888312