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

Sook Heui Jung

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 $f$.

Keywords


harmonic mapping, minimal surface.

Subject classification

30C45, 30C99.

Sponsor(s)

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

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References


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