黎曼映射定理

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 $\mathbb{C}$ 的单连通开子集。

设 $D := \{z \in \mathbb{C} : |z| < 1 \}$ 为开圆盘， $\Omega \subset \mathbb{C}$ 为单连通开子集。若 $\Omega \neq \mathbb{C}$ ，则存在一对一的全纯映射 $f: \Omega \to D$ ，使 $f^{-1}: D \to \Omega$ 亦全纯。换言之， $\Omega$ 与 $D$ 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。

单词	Riemann mapping theorem
释义	Riemann mapping theorem 中文百科黎曼映射定理在数学中，黎曼映射定理是复分析最深刻的定理之一，此定理分类了 $\mathbb{C}$ 的单连通开子集。设 $D := \{z \in \mathbb{C} : \|z\| < 1 \}$ 为开圆盘， $\Omega \subset \mathbb{C}$ 为单连通开子集。若 $\Omega \neq \mathbb{C}$ ，则存在一对一的全纯映射 $f: \Omega \to D$ ，使 $f^{-1}: D \to \Omega$ 亦全纯。换言之， $\Omega$ 与 $D$ 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。英语百科 Riemann mapping theorem 黎曼映射定理 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
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Riemann mapping theorem

黎曼映射定理

Riemann mapping theorem 黎曼映射定理