The two-dimensional analogue of the catenary

Reinhold Böhme, Stefan Hildebrandt and Engelbert Tausch

Vol. 88 (1980), No. 2, 247–278

DOI: 10.2140/pjm.1980.88.247

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