Non-univalent harmonic maps homotopic to diffeomorphisms.
type: Item
instance of: scholarly article
title: Non-univalent harmonic maps homotopic to diffeomorphisms.
zbMATH Open document ID: 1035.58014
author: M. S. Raghunathan
author: F. Thomas Farrell
author: Pedro Ontaneda
published in: Journal of Differential Geometry
publication date: 2002-08-15T00:00:00Z
review text: This paper answers, by the negative, a question of S.T. Yau, by showing that a harmonic map homotopic to a diffeomorphism between negatively curved compact manifolds is not necessarily univalent (i.e. one-to-one or injective). \newline This is achieved by constructing, in any dimension at least six, a pair of purpose-built closed connected negatively curved manifolds, together with a diffeomorphism, which, by Eells-Sampson's theorem, admits a unique homotopic harmonic map, shown to be non-univalent. The construction of these manifolds is based on the intricate building of an arithmetic group and the corresponding quotient manifolds.
reviewed by: Eric Loubeau
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 53C43
Mathematics Subject Classification ID: 57R50
zbMATH DE Number: 1782640
zbMATH Keywords: harmonic maps
zbMATH Keywords: univalent maps
zbMATH Keywords: arithmetic groups
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214341646
OpenAlex ID: W1556228182
Wikidata QID: Q115194495
DOI: 10.4310/JDG/1214341646
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description: scientific article; zbMATH DE number 1782640