scholarly journals Bi-lipschicity of quasiconformal harmonic mappings in the plane

Filomat ◽  
2009 ◽  
Vol 23 (1) ◽  
pp. 85-89 ◽  
Author(s):  
Vesna Manojlovic
Keyword(s):  
Harmonic Mappings ◽  
Quasihyperbolic Metric ◽  
The Quasihyperbolic Metric

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

Quasi-isometricity and equivalent moduli of continuity of planar 1/|ω|2-harmonic mappings

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 335-345
Author(s):  
Qi Yi ◽  
Shi Qingtian
Keyword(s):  
Quasiconformal Mapping ◽  
Connected Domain ◽  
Quasiregular Mapping ◽  
Harmonic Mappings ◽  
Moduli Of Continuity ◽  
Lipschitz Continuous ◽  
Quasihyperbolic Metric ◽  
Simply Connected Domain ◽  
Simply Connected

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.

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