多角形区域共形映射及其应用

The Conformal Mapping of Polygonal Domain and Its Application

摘要: 共形映射是复分析的重要部分，它广泛的应用于科技领域的各个方面。本文首先分析了如何从多角形区域共形映射为上半平面的方法，给出了克里斯托费尔–施瓦茨变换及其推广形式，并对推广的广义多角形的克里斯托费尔–施瓦茨变换进行了实例分析，讨论了广义多角形共形映射的求法。

Abstract: The conformal mapping is the important part of Function of Complex Variables and it has been widely used in various areas of science and technology. Firstly, this paper presents the conformal mapping of the upper half-plane onto polygonal domain and gives the Christoffel-Schwarz transform and its generalizing forms. And then we give the examples of the conformal mapping of the upper half-plane onto polygonal domain.>