Quasiconformal extensions of starlike harmonic mappings in the unit disc

Hidetaka Hamada; Tatsuhiro Honda; Kwang Ho Shon

doi:10.4134/BKMS.2013.50.4.1377

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(4): 1377-1387

Printed July 1, 2013

https://doi.org/10.4134/BKMS.2013.50.4.1377

Quasiconformal extensions of starlike harmonic mappings in the unit disc

Hidetaka Hamada, Tatsuhiro Honda, and Kwang Ho Shon

Kyushu Sangyo University, Hiroshima Institute of Technology, Pusan National University

Abstract

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Abstract

Let $f$ be a harmonic mapping on the unit disc $\Delta$ in $\C$. We give some condition for $f$ to be a quasiconformal homeomorphism on $\Delta$ and to have a quasiconformal extension to the whole plane $\overline{\C}$. We also obtain quasiconformal extension results for starlike harmonic mappings of order $\alpha\in(0,1)$.

Keywords: harmonic mapping, quasiconformal extension, starlike domain

MSC numbers: Primary 30C62, 30C45