Planar harmonic mappings

1990 ◽  
pp. 171-176 ◽  
Author(s):  
Glenn Schober
Keyword(s):  
Harmonic Mappings ◽  
Planar Harmonic Mappings

scholarly journals Distortion and covering theorems of pluriharmonic mappings

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2749-2762
Author(s):  
Shaolin Chen ◽  
Saminathan Ponnusamy
Keyword(s):  
Analytic Functions ◽  
Harmonic Mappings ◽  
Classical Approach ◽  
Covering Theorems ◽  
Linear Invariant ◽  
Planar Harmonic Mappings

The linear-invariant families of analytic functions make it possible to obtain well-known results to broader classes of functions, and are often helpful in obtaining simpler proofs along with new results. Based on this classical approach due to Pommerenke, properties (such as bounds for the derivative, covering and distortion) of a corresponding class of locally quasiconformal and planar harmonic mappings are established by Starkov. Motivated by these works, in this paper, we mainly investigate distortion and covering theorems on some classes of pluriharmonic mappings.

scholarly journals Bloch constants for planar harmonic mappings

2000 ◽  
Vol 128 (11) ◽  
pp. 3231-3240 ◽  
Author(s):  
Huaihui Chen ◽  
P. M. Gauthier ◽  
W. Hengartner
Keyword(s):  
Harmonic Mappings ◽  
Planar Harmonic Mappings

scholarly journals Lengths, areas and Lipschitz-type spaces of planar harmonic mappings

2015 ◽  
Vol 115 ◽  
pp. 62-70 ◽  
Author(s):  
Shaolin Chen ◽  
Saminathan Ponnusamy ◽  
Antti Rasila
Keyword(s):  
Harmonic Mappings ◽  
Type Spaces ◽  
Planar Harmonic Mappings
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