Harmonic mapping related with the minimal surface generated by analytic functions
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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 $f$.
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 $f$.
참고문헌 (7)
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