The General Problem of Douglas

Richard Courant
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Richard Courant: New York University, Institute for Mathematics and Mechanics

Chapter Chapter IV in Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces, 1950, pp 141-166 from Springer

Abstract: Abstract In contours γ consisting of several closed curves, soap film experi­ments produce multiply connected minimal surfaces, as for example in the classical case of surfaces of revolution of least area. Moreover, for suitable contours γ, soap film experiments indicate the existence of minimal surfaces of higher topological structure such as surfaces not of genus zero or non-orientable surfaces,1 see Figures 4.1 and 4.2. Such more complicated surfaces are formed by the soap film whenever they have greater stability—i. e. smaller area—than simply connected surfaces spanned in the same contour.

Keywords: Minimal Surface; Branch Point; Boundary Curve; Fundamental Domain; Parameter Domain (search for similar items in EconPapers)
Date: 1950
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DOI: 10.1007/978-1-4612-9917-2_5

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