在数学中，黎曼映射定理是复分析最深刻的定理之一，此定理分类了的单连通开子集。

设为开圆盘，为单连通开子集。若，则存在一对一的全纯映射，使亦全纯。换言之，与 双全纯同构。

注意到二维的全纯映射不外乎保持定向的共形映射，它保持角度与定向不变。

In complex analysis, the Riemann mapping theorem states that if U is a non-empty simply connected open subset of the complex number plane C which is not all of C, then there exists a biholomorphic mapping f (i.e. a bijective holomorphic mapping whose inverse is also holomorphic) from U onto the open unit disk