Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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HARMONIC MAPPING RELATED WITH THE MINIMAL SURFACE GENERATED BY ANALYTIC FUNCTIONS

  • Received : 2015.07.12
  • Accepted : 2015.09.10
  • Published : 2015.09.30
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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 $\mathbb{D}=\{z :{\mid}z{\mid}<1\}$, where -1 < a < 1. From these functions we obtain the regular simply-connected minimal surface $S=\{(u(z),\;{\nu}(z),\;H(z)):z{\in}\mathbb{D}\}$ in $E^3$ and the harmonic function $f=u+i{\nu}$ defined on $\mathbb{D}$, and then we investigate properties of the minimal surface S and the harmonic function f.

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References

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