Riemann's mapping theorem

Japanese: Riemann's mapping theorem(英語表記)Riemannsmappingtheorem
Riemann's mapping theorem

...The Schwarz–Christoffel formula is used to express the function that conformally maps a half-plane onto the interior or exterior of a polygon. Riemann (1851) claimed that any simply connected domain with two or more boundary points can always be conformally mapped onto the unit disk (Riemann's mapping theorem). His proof was flawed, but was completely proved by W. Osgood (1900) and H. Poincaré (1907). ...

*Some of the terminology that refers to "Riemann's mapping theorem" is listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…半平面を多角形の内部または外部の上に等角写像する関数を表すのに,シュワルツ=クリストッフェル公式がある。 リーマン(1851)は,二つ以上の境界点をもつ単連結領域は,つねに単位円板の上に等角写像できることを主張した(リーマンの写像定理Riemann’s mapping theorem)。彼の証明には欠陥があったが,オズグッドW.Osgood(1900),H.ポアンカレ(1907)によって完全に証明された。…

※「Riemann's mapping theorem」について言及している用語解説の一部を掲載しています。

出典|株式会社平凡社世界大百科事典 第2版について | 情報

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