\(p\)-harmonic morphisms, minimal foliations, and rigidity of metrics
type: Item
instance of: scholarly article
title: \(p\)-harmonic morphisms, minimal foliations, and rigidity of metrics
zbMATH Open document ID: 1077.58008
author: Ye-Lin Ou
published in: Journal of Geometry and Physics
publication date: 2005-06-13T00:00:00Z
review text: The paper contains a mixture of results about \(p\)-harmonic morphisms. First, there are two classification results, which are variations of their harmonic (i.e., \(p=2\)) counterparts: \(p\)-harmonic morphisms of twisted product type from complete simply connected manifolds are classified [generalizing \textit{M.~Svensson}, J. Lond. Math. Soc. (2) 68, 781--794 (2003; Zbl 1062.53020)], as well as polynomial and holomorphic \(p\)-harmonic morphisms [generalizing \textit{S.~Gudmundsson} and \textit{R.~Sigurdsson}, Potential Anal. 2, 295--298 (1993; Zbl 0783.58015)]. Moreover, \(p\)-harmonic functions (including the case \(p=1\)) whose level surfaces produce minimal foliations are characterized, generalizing results from [\textit{P.~Baird} and \textit{J.~Eells}, Lect. Notes Math. 894, 1--25 (1981; Zbl 0485.58008)]. It is also proven that if a complete conformally non-flat metric \(g=F^{-2}\sum_{i=1}^m dx_i^2\) on an open subset of \(\mathbb{R}^m\) admits one Riemannian or \(m{-}1\) minimal coordinate plane foliations, then it must be the hyperbolic metric up to a homothety.
reviewed by: Andreas Gastel
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 53C43
Mathematics Subject Classification ID: 53C24
zbMATH DE Number: 2175229
zbMATH Keywords: \(p\)-harmonic morphisms
zbMATH Keywords: \(1\)-harmonic functions
zbMATH Keywords: minimal foliations
MaRDI profile type: Publication
full work available at URL: j.geomphys.2004.04.002
OpenAlex ID: W2003657712
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DOI: 10.1016/J.GEOMPHYS.2004.04.002
description: scientific article; zbMATH DE number 2175229