On values of Gauss maps of complete minimal surfaces on annular ends
type: Item
instance of: scholarly article
title: On values of Gauss maps of complete minimal surfaces on annular ends
zbMATH Open document ID: 0760.53005
DOI: 10.1007/BF01445210
author: Shu-Jung Kao
published in: Mathematische Annalen
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/164869
review text: Let \(M\) be a complete non-flat minimal surface in \(\mathbb{R}^ 3\), and \(G\) be the Gauß map of \(M\). In 1990, Mo and Osserman proved that \(G\) assumes every value infinitely often with at most four exceptions, unless the surface has finite total curvature. In the present paper the author shows that the Gauß map of an annular end has the same properties. This is a local version of the theorem above.
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 59960
zbMATH Keywords: minimal surface
zbMATH Keywords: Gauß map
zbMATH Keywords: finite total curvature
reviewed by: Fritz Gackstatter
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 59960