Korean J. Math. Vol. 23 No. 3 (2015) pp.439-446
DOI: https://doi.org/10.11568/kjm.2015.23.3.439

Harmonic mapping related with the minimal surface generated by analytic functions

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Published: Sep 30, 2015
Keywords:
harmonic mapping, minimal surface.
Mathematics Subject Classification:
30C45, 30C99.

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Sook Heui Jung
Department of Mathematics Seoul Women’s University Seoul 01797, Korea

Abstract

In this paper we consider the meromorphic function $G(z)$ with a pole of order $1$ at $-a$ and analytic function $F(z)$ with a zero $-a$ of order 2 in ${\Bbb D}= \{ z : |z| < 1 \}$, where $-1<a<1.$ From these functions we obtain the regular simply-connected minimal surface $S=\{(u(z),v(z), H(z)) : z \in {\Bbb D} \}$ in $E^3$ and the harmonic function $ f = u + iv $ defined on $\Bbb D$, and then we investigate properties of the minimal surface $S$ and the harmonic function $f$.


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Supporting Agencies

This work was supported by a research grant from Seoul Women’s Univer- sity(2014).

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