On helicoidal ends of minimal surfaces
type: Item
instance of: scholarly article
title: On helicoidal ends of minimal surfaces
zbMATH Open document ID: 0873.53002
DOI: 10.1007/BF02108306
author: Pascal Romon
published in: Annals of Global Analysis and Geometry
publication date: 1997-10-26T00:00:00Z
review text: Let \(M\) be a properly embedded minimal plane in \(\mathbb{R}^3\) which meets all but a finite number of horizontal planes (up to a rotation in space) transversally in a single open curve. If the Gauss map \(g\), seen as a meromorphic map through the stereographic projection, has finite order (in the sense of Nevanlinna) then the minimal surface is the helicoid or the plane.
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 762879
zbMATH Keywords: rigidity theorem
zbMATH Keywords: helicoid
zbMATH Keywords: Gauss map
zbMATH Keywords: finite order
MaRDI profile type: Publication
cites work: On a Conjecture of Nitsche
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cites work: Adding handles to the helicoid
cites work: Q3873112
cites work: The geometry of periodic minimal surfaces
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cites work: A rigidity theorem for Riemann's minimal surfaces
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cites work: Minimal surfaces of finite type
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full work available at URL: https://doi.org/10.1007/bf02108306
OpenAlex ID: W1987920292
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description: scientific article; zbMATH DE number 762879