QUASICONFORMAL EXTENSIONS OF STARLIKE HARMONIC MAPPINGS IN THE UNIT DISC

Title & Authors
QUASICONFORMAL EXTENSIONS OF STARLIKE HARMONIC MAPPINGS IN THE UNIT DISC
Hamada, Hidetaka; Honda, Tatsuhiro; Shon, Kwang Ho;

Abstract
Let $\small{f}$ be a harmonic mapping on the unit disc $\small{{\Delta}}$ in $\small{\mathbb{C}}$. We give some condition for $\small{f}$ to be a quasiconformal homeomorphism on $\small{{\Delta}}$ and to have a quasiconformal extension to the whole plane $\small{\bar{\mathbb{C}}}$. We also obtain quasiconformal extension results for starlike harmonic mappings of order $\small{{\alpha}{\in}(0,1)}$.
Keywords
harmonic mapping;quasiconformal extension;starlike domain;
Language
English
Cited by
1.
Pluriharmonic mappings in Cn and complex Banach spaces, Journal of Mathematical Analysis and Applications, 2015, 426, 2, 635
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