A theorem of Liouville type for \(p\)-harmonic morphisms
type: Item
instance of: scholarly article
title: A theorem of Liouville type for \(p\)-harmonic morphisms
zbMATH Open document ID: 1038.58013
DOI: 10.1023/A:1026343820908
author: Gundon Choi
author: Gabjin Yun
published in: Geometriae Dedicata
publication date: 2004-01-14T00:00:00Z
review text: This paper generalizes a remark on harmonic morphisms proved by the same authors [Geom. Dedicata 84, 179--182 (2001; Zbl 0980.58010)] to the case of \(p\)-harmonic morphisms, \(p\geq2\). It is proved that any \(p\)-harmonic morphism from a complete noncompact Riemannian manifold of nonnegative Ricci curvature to a Riemannian manifold of nonpositive scalar curvature has to be constant if it has finite \(p\)-energy or finite \((2p-2)\)-energy. The proof uses the Bochner technique.
reviewed by: Andreas Gastel
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 2027204
zbMATH Keywords: harmonic morphisms
zbMATH Keywords: Bochner formula
zbMATH Keywords: Liouville theorem
MaRDI profile type: Publication
full work available at URL: a:1026343820908
OpenAlex ID: W4248716811
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description: scientific article; zbMATH DE number 2027204