Complete nonorientable minimal surfaces and symmetries
type: Item
instance of: scholarly article
title: Complete nonorientable minimal surfaces and symmetries
zbMATH Open document ID: 0861.53006
DOI: 10.1215/S0012-7094-95-07917-4
author: Francisco Martín
author: Francisco J. López
published in: Duke Mathematical Journal
publication date: 1997-04-24T00:00:00Z
review text: The authors present new examples of complete nonorientable minimal surfaces in \(\mathbb{R}^3\) with only one end and finite total curvature. To be more precise, they construct infinite families of such surfaces, calculate their Euler-Poincaré characteristic as well as their total curvature, and describe their symmetry groups. Moreover, they show that these surfaces are unique and maximal with respect to the total curvature. The main tool for the construction is the Weierstraß representation formula. A special case is the complete minimal once-punctured Klein bottle with total curvature \(-8\pi\) originally discovered by the first author [ibid. 71, No. 1, 23-30 (1993; Zbl 0796.53006)].
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 878411
zbMATH Keywords: new examples
zbMATH Keywords: complete nonorientable minimal surfaces
zbMATH Keywords: one end
zbMATH Keywords: finite total curvature
MaRDI profile type: Publication
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full work available at URL: s0012-7094-95-07917-4
OpenAlex ID: W1492226251
description: scientific article; zbMATH DE number 878411