两类象域为多边形的单叶调和映射

Two Kinds of Mappings of Univalent Harmonic Functions onto Polygon

我们给出当ａ（ｚ）＝ｅｉθ（（ｚ－α）／（１－αｚ））ｍ，ｍ＝１，２时存在将单位圆盘单叶调和保向地映射为已知的多边形并且满足给定的Ｂｅｌｔｒａｍｉ方程ｆｚ＝ａ（ｚ）ｆｚ的映射的充分必要条件．

It is given that the sufficient and necessary conditions of existence of the univalent harmonic orientationpreserving mapping f(z) which satisfies the equation f =a(z)f z for given Beltrami coefficient a(z)= e iθ ((z-α)/(1-z)) m,m=1,2 and maps unit disk U onto a given polygon P .