Liouville type theorems of \(f\)-harmonic maps with potential
type: Item
instance of: scholarly article
title: Liouville type theorems of \(f\)-harmonic maps with potential
zbMATH Open document ID: 1317.58018
author: Shuxiang Feng
author: Yingbo Han
published in: Results in Mathematics
publication date: 2014-11-17T00:00:00Z
review text: Two different generalizations of harmonic maps between Riemannian manifolds are put together here. As a variant of \(\int|Du(x)|^2\,dx\), the functional \(\int f(x)|Du(x)|^2\,dx\) can be considered with a positive function \(f\); its stationary points are called \(f\)-harmonic maps. If the domain dimension is not \(2\), this is not really more general, since the factor can be interpreted as the effect of a conformal change of metrics, but nevertheless the paper allows that case. The other variant is that of adding a potential to the functional. This has been done in connection with harmonic maps (the \(f\equiv1\) case), and is generalized here to nonconstant \(f\). The paper combines established methods for both \(f\)-harmonic maps and harmonic maps with potential, and derives standard results like monotonicity formulas and Liouville type theorems.
reviewed by: Andreas Gastel
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 35B53
zbMATH DE Number: 6370028
zbMATH Keywords: \(f\)-harmonic maps with potential
zbMATH Keywords: \(f\)-stress-energy tensor
zbMATH Keywords: monotonicity formula
zbMATH Keywords: Liouville type theorem
MaRDI profile type: Publication
full work available at URL: s00025-014-0363-9
OpenAlex ID: W2018703813
cites work: Stress-energy tensors and the Lichnerowicz Laplacian
cites work: \(f\)-harmonic maps which map the boundary of the domain to one point in the target
cites work: Q4954278
cites work: On vanishing theorems for vector bundle valued \(p\)-forms and their applications
cites work: A Report on Harmonic Maps
cites work: Harmonic maps with potential
cites work: New comparison theorems in Riemannian geometry
cites work: Q4929885
cites work: \(f\)-harmonic maps of doubly warped product manifolds
cites work: Monotonicity formulae and Liouville theorems of harmonic maps with potential
cites work: Stability and quantum phenomenon and Liouville theorems of \(p\)-harmonic maps with potential
DOI: 10.1007/S00025-014-0363-9
description: scientific article; zbMATH DE number 6370028