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Quasiconformal extensions of starlike harmonic mappings in the unit disc
Hidetaka Hamada,손광호,Tatsuhiro Honda 대한수학회 2013 대한수학회보 Vol.50 No.4
Let f be a harmonic mapping on the unit disc Δ in C. We give some condition for f to be a quasiconformal homeomorphism on Δ and to have a quasiconformal extension to the whole plane C. We also obtain quasiconformal extension results for starlike harmonic mappings of order α∈2 (0, 1).
QUASICONFORMAL EXTENSIONS OF STARLIKE HARMONIC MAPPINGS IN THE UNIT DISC
Hamada, Hidetaka,Honda, Tatsuhiro,Shon, Kwang Ho Korean Mathematical Society 2013 대한수학회보 Vol.50 No.4
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 ${\alpha}{\in}(0,1)$.