In this paper it was found the conditions of existence of the univalent harmonic orientation-preserving mapping f(z) which satisfies the equation =a(z)f_z for given Beltrami coefficient a(z) and maps unit disk U onto a given polygon P.

• 本文对于给定的Betrami系数a(z)找到了存在将单位圆盘U映射为给定的多边形P并且满足方程的单叶调和保向映射函数f(z)的条件。