Some conformal properties of \(p\)-harmonic maps and a regularity for sphere-valued \(p\)-harmonic maps
type: Item
instance of: scholarly article
title: Some conformal properties of \(p\)-harmonic maps and a regularity for sphere-valued \(p\)-harmonic maps
zbMATH Open document ID: 0817.58011
author: Hiroshi Takeuchi
published in: Journal of the Mathematical Society of Japan
publication date: 1995-07-31T00:00:00Z
review text: Let \(u : M \to N\) be a smooth map between Riemannian manifolds and \(p\) a real number, \(1 < p < +\infty\). We say that \(u\) is a \(p\)-harmonic map if it is a critical point of the \(p\)-energy functional \(\int_ \Omega | du|^ p\) for every compact domain \(\Omega \subset M\). The aim of this paper is to study conformal properties of \(p\)-harmonic maps and the regularity problem for sphere-valued \(p\)-harmonic maps. It should be mentioned that this article -- which is a good reference for people wanting to learn the standard Riemannian geometric facts about \(p\)-harmonic maps -- has some overlapping with an article of \textit{P. Baird} and \textit{S. Gudmundsson} [Math. Ann. 294, No. 4, 611-624 (1992; Zbl 0757.53031)].
reviewed by: Andrea Ratto
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 711437
zbMATH Keywords: \(p\)-harmonic maps
zbMATH Keywords: conformal maps
zbMATH Keywords: regularity
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04620217
OpenAlex ID: W2066342121
DOI: 10.2969/JMSJ/04620217
description: scientific article; zbMATH DE number 711437