Uniqueness of the Riemann minimal examples
type: Item
instance of: scholarly article
title: Uniqueness of the Riemann minimal examples
zbMATH Open document ID: 0916.53004
author: Joaquín Pérez
author: Antonio Ros
author: William H. III Meeks
published in: Inventiones Mathematicae
publication date: 1999-07-15T00:00:00Z
review text: Riemann classified all minimal surfaces in \(\mathbb{R}^3\) that are foliated by circles and straight lines in horizontal planes. The only such surfaces are the plane, the helicoid, and a one-parameter family of what are now called Riemann minimal examples. In the paper under review, the authors show that the only properly embedded periodic minimal surfaces in \(\mathbb{R}^3\) of genus zero with two limit ends are the Riemann minimal examples.
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 1186165
zbMATH Keywords: Euclidean 3-space
zbMATH Keywords: periodic minimal surfaces
zbMATH Keywords: genus zero
zbMATH Keywords: limit ends
reviewed by: Thomas Hasanis
MaRDI profile type: Publication
full work available at URL: s002220050241
OpenAlex ID: W2039574292
DOI: 10.1007/S002220050241
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description: scientific article; zbMATH DE number 1186165