A rigidity theorem for Riemann's minimal surfaces

Abstract : 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.
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Pascal Romon. A rigidity theorem for Riemann's minimal surfaces. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 1993, 43 (2), pp.485. ⟨10.5802/aif.1342⟩. ⟨hal-00862672⟩

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