A rigidity theorem for Riemann's minimal surfaces
We describe first the analytic structure of Riemann's examples of singly- periodic minimal surfaces; we also characterize them as extensions of minimal annuli bounded by parallel straight lines between parallel planes. We then prove their uniqueness as solutions of the perturbed problem of a punctured annulus, and we present standard methods for determining finite total curvature periodic minimal surfaces and solving the period problems.
scientific article; zbMATH DE number 425541