双调和映照的单叶性与线性连结性

假设F(z)=|z|²g(z)+h(z)为单位圆盘D={z||z|<1}上的双调和映照,其中,0z(z)|-|h₍-overz)(z)||,|g_z(z)|+|g₍-overz)(z)|≤Λ,z∈D.研究F(z)的单叶性、F(D)线性连结性、h(z)的单叶性与 h(D)线性连结性问题,得到h(z)与F(z)之间的相互对应关系.

Univalence and Linear Connetivity of Biharmonic Mappings

Suppose that F(z)=|z|²g(z)+h(z)is a biharmonic mapping on the unit disk D={z||z|<1}, and 0z(z)|-|h₍-overz)(z)||,|g_z(z)|+|g₍-overz)(z)|≤Λ,z∈D, we consider the relation between h(z)and F(z)for their univalence and linear connetivity of h(D)and F(D)under some conditions, we establish that if h(z)is univalent and h(D)is linear connected domain, so are F(z)and F(D), and vice versa.