Vol. 88, No. 2, 1980

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The two-dimensional analogue of the catenary

Reinhold Böhme, Stefan Hildebrandt and Engelbert Tausch

Vol. 88 (1980), No. 2, 247–278
Abstract

In this paper we consider the following isoperimetric problem: let Γ be a prescribed Jordan curve in R3. Determine a surface of given area spanning Γ, which has minimal potential energy under gravitational forces. This will be of importance for the construction of “perfect domes.”

Mathematical Subject Classification
Primary: 49F99, 49F99
Milestones
Received: 3 March 1980
Published: 1 June 1980
Authors
Reinhold Böhme
Stefan Hildebrandt
Engelbert Tausch