quasihyperbolic metric
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Author(s):  
Jesús Gonzalo ◽  
Ana Portilla ◽  
Jose M. Rodríguez ◽  
Eva Tourís

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 335-345
Author(s):  
Qi Yi ◽  
Shi Qingtian

In this paper, we prove that 1/|?|2-harmonic quasiconformal mapping is bi-Lipschitz continuous with respect to quasihyperbolic metric on every proper domain of C\{0}. Hence, it is hyperbolic quasi-isometry in every simply connected domain on C\{0}, which generalized the result obtained in [14]. Meanwhile, the equivalent moduli of continuity for 1/|?|2-harmonic quasiregular mapping are discussed as a by-product.


Filomat ◽  
2009 ◽  
Vol 23 (1) ◽  
pp. 85-89 ◽  
Author(s):  
Vesna Manojlovic

We show that quasiconformal harmonic mappings on the proper domains in R2 are bi-Lipschitz with respect to the quasihyperbolic metric. .


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