• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1377-1387
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• 2013

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 ${\alpha}{\in}(0,1)$.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.39-44
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• 2000

In [2], D. Gaier has given an estimate of conformal mappings near the boundary. In this paper, we generalize for the K-quasiconformal mapping the corresponding result.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.865-869
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• 2012

In [2], D. Gaier has given an estimates of harmonic measure. In this paper, we generalize for the K-quasiconformal mapping the corresponding result.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1419-1431
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• 2018

Let $f=h+{\bar{g}}$ be a harmonic mapping of the unit disk ${\mathbb{D}}$ with the holomorphic part h satisfying that h is injective and $h({\mathbb{D}})$ is an M-linearly connected domain. In this paper, we obtain the sufficient and necessary conditions for f to be bi-Lipschitz, which is in particular, quasiconformal. Moreover, some distortion theorems are also obtained.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.359-366
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• 1996

In this paper, we provide two Teichm$\ddot{u}$ller extremal mappings of the unit disk, having different boundary values but the same dilatation.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.243-250
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• 2020

Hardy and Littlewood found a relation between the smoothness of the radial limit of an analytic function on the unit disk D ⊂ ℂ and the growth of its derivative. It is reasonable to expect an analytic function to be smooth on the boundary if its derivative grows slowly, and conversely. Gehring and Martio showed this principle for uniform domains in ℝ². Astala and Gehring proved quasiconformal analogue of this principle for uniform domains in ℝⁿ. We consider α-quasihyperbolic metric, k^α_D and we extend it to proper domains in ℝⁿ.