A rigidity theorem for Riemann's minimal surfaces
type: Item
instance of: scholarly article
title: A rigidity theorem for Riemann's minimal surfaces
zbMATH Open document ID: 0780.53011
author: Pascal Romon
publication date: 1993-12-06T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75006
review text: 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.
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 425541
zbMATH Keywords: singly-periodic minimal surfaces
zbMATH Keywords: minimal annuli
zbMATH Keywords: finite total curvature
MaRDI profile type: Publication
OpenAlex ID: W1964470488
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cites work: Q3873112
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cites work: Some uniqueness and nonexistence theorems for embedded minimal surfaces
cites work: On the minimal surfaces of Riemann
DOI: 10.5802/AIF.1342
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 425541