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The problem in Calculus of Variations to find the Minimal Surface of a boundary with specified constraints. In general, there may be one, multiple, or no Minimal Surfaces spanning a given closed curve in space.
See also Calculus of Variations, Minimal Surface
References
Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 48-49, 1989.
Stuwe, M. Plateau's Problem and the Calculus of Variations. Princeton, NJ: Princeton University Press, 1989.