保角映射(又称保形变换或共形映照)是解析函数理论中最重要的概念之一。关于保角映射的定义,各书常以不同的形式给出,本文主要研究它们之间的等价性。 (一) 为了下面行文的方便,先扼要的叙述一下复变函数导数的几何意义。设函数W=f(Z)在Z_0解析且f'(Z_0)≠0,考虑过Z_0的一条简单光滑曲线C_1: Conformal mapping (also known as conformal mapping or conformal mapping) is one of the most important concepts in analytical function theory. On the definition of conformal mapping, the book is often given in different forms, this paper focuses on the equivalence between them. (A) In order to facilitate the following text, the first brief description of the geometric meanings of the complex function derivative. Let the function W = f (Z) be a simple smooth curve with Z_0 parsing and f '(Z_0) ≠ 0 considering Z_0. C_1: