两连域保角映射成环域的方法

本文论述一种把型区域保角映射成环域的方法.其要点是将问题转化为Dirichlet问题,并证明该映像函数之实部应满足本文所示的边界条件,进而依据两连域上定义的调和函数的单值特性确定环域的内半径.映像函数的虚部可由Cauchy-Riemann条件得到,由此产生的积分常数仅影响映像点的幅角,并可由一一对应的映像来确定.不失其一般性,本方法可将由矩形拼成的复杂两连域保角映射成环域.笔者还对本方法作了电算,证明本方法可靠、经济、结果附有表格.

A Method for Conforma! Mapping of a Two-Connected Region onto an Annuius

This paper presents a method for conformal mapping of a two-connected region onto an annulus. The principle of the method is to find a holomorphic function, the real part of which should be a harmonic function satisfying certain boundary conditions.The key for solving the problem is to determine the inner radius of annulus. According to the theory of complex functions we shall determine it from the condition that the line integral predicted along multiple closed paths should be zero.It is then easy to see that the imaginary part can directly be obtained with the aid of Cauchy-Riemann equations. The unknown integral constants can also be derived by using the one-to-one mapping of previous region onto annulus.Without loss of generality, the method may be used to conformally map other two-connected regions onto an annulus.