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A SCHWARZ LEMMA FOR $V$-HARMONIC MAPS AND THEIR APPLICATIONS

Part of: Holomorphic mappings and correspondences Variational problems in infinite-dimensional spaces Geometric function theory Complex manifolds

Published online by Cambridge University Press:  17 August 2017

QUN CHEN  and
GUANGWEN ZHAO
QUN CHEN*
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China email qunchen@whu.edu.cn
GUANGWEN ZHAO
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, PR China email gwzhao@whu.edu.cn
*
✉qunchen@whu.edu.cn
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Abstract

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We establish a Schwarz lemma for $V$-harmonic maps of generalised dilatation between Riemannian manifolds. We apply the result to obtain corresponding results for Weyl harmonic maps of generalised dilatation from conformal Weyl manifolds to Riemannian manifolds and holomorphic maps from almost Hermitian manifolds to quasi-Kähler and almost Kähler manifolds.

Keywords

Schwarz lemmaV-harmonic mapOmori–Yau maximum principleholomorphic mapalmost Hermitian manifold

MSC classification

Primary: 58E20: Harmonic maps , etc.
Secondary: 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination 32Q60: Almost complex manifolds 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 3 , December 2017 , pp. 504 - 512
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

This work is partially supported by the NSF China (Grant number 11571259).

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