• 대한수학회보
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• 제55권3호
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• pp.819-835
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• 2018

Let $f=h+{\bar{g}}$ be a normalized harmonic mapping in the unit disk $\mathbb{D}$. In this paper, we obtain the sharp radius of univalence, fully starlikeness and fully convexity of the harmonic linear differential operators $D^{\epsilon}{_f}=zf_z-{\epsilon}{\bar{z}}f_{\bar{z}}({\mid}{\epsilon}{\mid}=1)$ and $F_{\lambda}(z)=(1-{\lambda)f+{\lambda}D^{\epsilon}{_f}(0{\leq}{\lambda}{\leq}1)$ when the coefficients of h and g satisfy harmonic Bieberbach coefficients conjecture conditions. Similar problems are also solved when the coefficients of h and g satisfy the corresponding necessary conditions of the harmonic convex function $f=h+{\bar{g}}$. All results are sharp. Some of the results are motivated by the work of Kalaj et al. [8].

• Korean Journal of Mathematics
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• 제11권2호
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• pp.79-84
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• 2003

In this paper, we obtain the sharp estimates for co-efficients of harmonic, orientation-preserving, univalent mappings defined on ${\Delta}=\{z:{\mid}z{\mid}>1\}$ when harmonic mappings are of bounded variation on ${\mid}z{\mid}=1$.

• 충청수학회지
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• 제16권2호
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• pp.31-41
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• 2003

In this paper, we will show that the bounds for coefficients of harmonic, orientation-preserving, univalent mappings f defined on ${\Delta}$ = {z : |z| > 1} with $f({\Delta})={\Delta}$ are sharp by finding extremal functions.

• 충청수학회지
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• 제19권4호
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• pp.313-318
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• 2006

In this paper, we study harmonic mappings related to the nonparametric minimal surfaces that lie over the upper halfplane.

• 대한수학회보
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• 제50권4호
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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 ${\alpha}{\in}(0,1)$.

• 대한수학회보
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• 제52권6호
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• pp.1925-1935
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• 2015

In this paper, we study right half-plane harmonic mappings $f_0$ and f, where $f_0$ is fIxed and f is such that its dilatation of a conformal automorphism of the unit disk. We obtain a sufficient condition for the convolution of such mappings to be convex in the direction of the real axis. The result of the paper is a generalization of the result of by Li and Ponnusamy [11], which itself originates from a problem posed by Dorff et al. in [7].

• Korean Journal of Mathematics
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• 제8권2호
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• pp.135-138
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• 2000

In this paper, we study harmonic orientation-preserving univalent mappings defined on ${\Delta}=\{z:{\mid}z{\mid}>1\}$ that are typically real.

• Korean Journal of Mathematics
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• 제10권1호
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• pp.1-3
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• 2002

In this paper, we obtain some coefficient bounds of harmonic, orientation-preserving, univalent mappings defined on ${\Delta}=\{z:{\mid}z{\mid}>1\}$.

• Korean Journal of Mathematics
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• 제4권1호
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• pp.65-70
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• 1996

In this note, we study a relation between harmonic maps and exponential harmonic maps, and we show existence of Yang-Mills connections.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권3호
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• pp.217-220
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• 2008

In this paper, we investigate the harmonic mappings that arise in connection with Scherk's surface and helicoid.