A generalization of a theorem of Delaunay on constant mean curvature surfaces. (English) Zbl 0799.53010

Davis, H. Ted (ed.) et al., Statistical thermodynamics and differential geometry of microstructured materials. Lectures presented at a workshop held from January 21-25, 1991. New York: Springer-Verlag. IMA Vol. Math. Appl. 51, 123-130 (1993).
The paper contains a classification of all complete constant mean curvature surfaces in \({\mathbb{R}}^ 3\) admitting a one-parameter group of isometries. To arrive at the classification the author notes that any such surface would give rise to a solution of a certain differential equation. The study of the asymptotic behaviour of solutions of this equation allows to decide completeness.
For the entire collection see [Zbl 0778.00020].
Reviewer: B.Opozda (Kraków)


53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature