A Liouville type theorem for \(p\)-harmonic maps
type: Item
instance of: scholarly article
title: A Liouville type theorem for \(p\)-harmonic maps
zbMATH Open document ID: 0914.58009
author: Nobumitsu Nakauchi
published in: Osaka Journal of Mathematics
publication date: 1998-11-02T00:00:00Z
review text: The author proves a Liouville type theorem for \(p\)-harmonic maps. Namely, considering the Riemannian manifolds \((M,g)\) and \((N,h)\), where \(M\) is complete, noncompact and has nonnegative Ricci curvature and \(N\) has nonpositive sectional curvature, a \(p\)-harmonic map \(u: M\to N\) of \(C^1_{\text{loc}}\)-class is shown to be constant if its energy \(E_p(u)\) is finite, within the general case \(p\geq 2\).
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 1217806
zbMATH Keywords: \(p\)-energy
zbMATH Keywords: \(p\)-harmonic maps
zbMATH Keywords: Ricci curvature
zbMATH Keywords: sectional curvature
reviewed by: Vladimir Balan
MaRDI profile type: Publication
Recommended article: Liouville type theorems for \(p\)-harmonic maps
Recommended article: Q4901549
Recommended article: LIOUVILLE TYPE THEOREM FOR p-HARMONIC MAPS II
Recommended article: Q4952877
Recommended article: A theorem of Liouville type for \(p\)-harmonic morphisms
Recommended article: Q4782991
Recommended article: A Liouville Theorem for Harmonic Maps
Recommended article: A Liouville theorem for harmonic maps
Recommended article: Liouville-type theorems of \(p\)-harmonic maps with free boundary values
Recommended article: Liouville type theorem for \((\mathcal{F},\mathcal{F}')_p\)-harmonic maps on foliations
description: scientific article; zbMATH DE number 1217806