# QUASICONFORMAL EXTENSIONS OF STARLIKE HARMONIC MAPPINGS IN THE UNIT DISC

• Hamada, Hidetaka (Faculty of Engineering Kyushu Sangyo University) ;
• Honda, Tatsuhiro (Faculty of Engineering Hiroshima Institute of Technology) ;
• Shon, Kwang Ho (Department of Mathematics Pusan National University)
• Published : 2013.07.31
• 76 10

#### Abstract

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

#### Keywords

harmonic mapping;quasiconformal extension;starlike domain

#### Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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1. Pluriharmonic mappings in Cn and complex Banach spaces vol.426, pp.2, 2015, https://doi.org/10.1016/j.jmaa.2015.01.052