×

zbMATH — the first resource for mathematics

Beyond Delaunay surfaces. (English) Zbl 1203.53007
Summary: An interesting class of axially symmetric surfaces, which generalizes Delaunay’s unduloids and provides solutions of the shape equation is described in explicit parametric form. This class provide the first analytical examples of surfaces with periodic curvatures studied by K. Kenmotsu and leads to some unexpected relationships among Jacobian elliptic functions and their integrals.

MSC:
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
PDF BibTeX XML Cite