A nonexistence theorem of proper harmonic morphisms between hyperbolic spaces
type: Item
instance of: scholarly article
title: A nonexistence theorem of proper harmonic morphisms between hyperbolic spaces
zbMATH Open document ID: 1016.58004
DOI: 10.1023/A:1020382228934
author: Xiaohuan Mo
author: Yuguang Shi
published in: Geometriae Dedicata
publication date: 2002-12-15T00:00:00Z
review text: Harmonic morphisms between Riemannian manifolds are harmonic maps which preserve germs of harmonic functions. It is proved that there is no harmonic morphism from any hyperbolic space to a lower-dimensional hyperbolic space which is proper and of class \(C^2\) up to the boundary. The proof is quite short. Besides simple properties of smooth proper maps at the boundary of hyperbolic space, it uses only the harmonicity equation in coordinates and the maximum principle for subharmonic functions.
reviewed by: Andreas Gastel
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 1845450
zbMATH Keywords: harmonic morphism
zbMATH Keywords: hyperbolic spaces
zbMATH Keywords: proper maps
MaRDI profile type: Publication
full work available at URL: a:1020382228934
OpenAlex ID: W14996095
description: scientific article; zbMATH DE number 1845450