Index and stability of harmonic Gauss maps
type: Item
instance of: scholarly article
title: Index and stability of harmonic Gauss maps
zbMATH Open document ID: 0727.58011
DOI: 10.1007/BF02571363
author: Bennett Palmer
published in: Mathematische Zeitschrift
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174244
review text: \textit{E. A. Ruh} [J. Differ. Geom. 4, 509-513 (1970; Zbl 0206.502)] had proved that an immersed surface \(M\subset E^ 3\) has constant mean curvature h if and only if its Gauss map \(\nu\) : \(M\to S^ 2\) is a harmonic map. The author proves the following interesting result: Theorem. Suppose that \(M\subset E^ 3\) is a compact surface of constant mean curvature and genus g. Then Index(\(\nu\))\(\geq (l\arg est\) integer \(< 1+g/2)\).
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 4201191
zbMATH Keywords: index
zbMATH Keywords: stability of harmonic Gauss maps
zbMATH Keywords: immersion
zbMATH Keywords: Kato's inequality
zbMATH Keywords: constant mean curvature
reviewed by: Michael Th. Rassias
MaRDI profile type: Publication
cites work: Asymptotic behaviour of non-parametric minimal hypersurfaces
cites work: The Second Variation Formula for Harmonic Mappings
description: scientific article; zbMATH DE number 4201191