scholarly journals A Schwarz lemma and a Liouville theorem for generalized harmonic maps

2022 ◽  
Vol 214 ◽  
pp. 112556
Author(s):  
Qun Chen ◽  
Kaipeng Li ◽  
Hongbing Qiu
Keyword(s):  
Liouville Theorem ◽  
Harmonic Maps ◽  
Schwarz Lemma

A SCHWARZ LEMMA FOR -HARMONIC MAPS AND THEIR APPLICATIONS

2017 ◽  
Vol 96 (3) ◽  
pp. 504-512 ◽  
Author(s):  
QUN CHEN ◽  
GUANGWEN ZHAO
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Maps ◽  
Schwarz Lemma ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Holomorphic Maps ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Almost Kähler

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.

scholarly journals A converse to the Schwarz lemma for planar harmonic maps

2021 ◽  
pp. 124908
Author(s):  
Ole Fredrik Brevig ◽  
Joaquim Ortega-Cerdà ◽  
Kristian Seip
Keyword(s):  
Harmonic Maps ◽  
Schwarz Lemma ◽  
The Schwarz Lemma
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