Liouville-type theorems for CC-harmonic maps from Riemannian manifolds to pseudo-Hermitian manifolds
type: Item
instance of: scholarly article
title: Liouville-type theorems for CC-harmonic maps from Riemannian manifolds to pseudo-Hermitian manifolds
zbMATH Open document ID: 1377.53050
author: Tian Chong
author: Yuxin Dong
author: Yibin Ren
published in: Annals of Global Analysis and Geometry
publication date: 2017-08-11T00:00:00Z
review text: In the reviewed paper the authors consider a map \(f:(M,g)\to (N,H(N),J,\theta)\) from a Riemannian manifold to a pseudo-Hermitian manifold and introduce a horizontal energy functional \(E_H(f)\) for the map. The map \(f\) is called a Carnot-Caratheodory harmonic map, or CC-harmonic map for simplicity, if it is a critical point of \(E_H(f)\) with respect to any horizontal variational vector field. The authors also introduce the stress-energy tensor \(S_{f,H}\) associated with the horizontal energy \(E_H(f)\) which is a useful tool to investigate the conservation law of CC-harmonic maps. They investigate the monotonicity of CC-harmonic maps and establish the monotonicity formulae for the horizontal energy of CC-harmonic maps. Consequently, the authors obtain some Liouville-type theorems.
reviewed by: Marian Hotloś
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 6759502
zbMATH Keywords: CC-harmonic map
zbMATH Keywords: horizontal energy functional
zbMATH Keywords: monotonicity formulae
zbMATH Keywords: Liouville-type results
MaRDI profile type: Publication
full work available at URL: s10455-017-9547-3
OpenAlex ID: W2587094500
Wikidata QID: Q115384569
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DOI: 10.1007/S10455-017-9547-3
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description: scientific article; zbMATH DE number 6759502