In this paper we prove a Radó type result showing that there is no univalent polyharmonic mapping of the unit disk onto the whole complex plane. We also establish a connection between the boundary functions of harmonic and biharmonic mappings. Finally, we show how a close-to-convex biharmonic mapping can be constructed from a convex harmonic mapping.

中文翻译：

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关于多谐映射的注释

在本文中，我们证明了一个 Radó 类型的结果，表明没有单位圆盘在整个复平面上的单价多谐映射。我们还在谐波和双谐波映射的边界函数之间建立了联系。最后，我们展示了如何从凸谐波映射构建接近凸的双调和映射。