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In mathematics, the uniformization theorem says that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere. In particular it implies that every Riemann surface admits a Riemannian metric of constant curvature. For compact Riemann surfaces, those with universal cover the unit disk are precisely the hyperbolic surfaces of genus greater than 1, all with non-abelian fundamental group; those with universal cover the complex plane are the Riemann surfaces of genus 1, namely the complex tori or elliptic curves with fundamental group Z2; and those with universal cover the Riemann sphere are those of genus zero, namely the Riemann sphere itself, with trivial fundamental group.

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  • Théorème d'uniformisation de Riemann
  • Uniformization theorem
  • Teorema di uniformizzazione di Riemann
  • 一意化定理
  • Uniformeringsstelling
  • 균일화 정리
  • 单值化定理
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  • En mathématiques, le théorème d'uniformisation de Riemann est un résultat de base dans la théorie des surfaces de Riemann, c'est-à-dire des variétés complexes de dimension 1. Il assure que toute surface de Riemann simplement connexe peut être mise en correspondance biholomorphe avec l'une des trois surfaces suivantes : le plan complexe C, le disque unité de ce plan, ou la sphère de Riemann, c'est-à-dire la droite projective complexe P1(C).
  • 一意化定理(uniformization theorem)とは、すべての単連結リーマン面は、開円板、複素平面、リーマン球面の 3つのうちのひとつに共形同値であるという定理である。特に、単連結リーマン面は(constant curvature)のリーマン計量を持つ。この定理は普遍被覆リーマン面を楕円型(正の曲率、正の曲がった曲率をもつ)、放物型(平坦)、双曲型(負曲率)として分類する。 一意化定理はリーマンの写像定理の平面の固有な単連結開部分集合から、任意の単連結はリーマン面への一般化である。 一意化定理は、任意の連結である第二可算の面の同様な結果、定数曲率のリーマン計量を与えることができることを意味している。
  • Il teorema di uniformizzazione di Riemann è un importante teorema di analisi complessa, dimostrato dal matematico Bernhard Riemann. Il teorema descrive un forte collegamento fra l'analisi complessa e la geometria differenziale per le superfici.
  • 복소해석학에서, 균일화 정리(均一化定理, uniformization theorem)는 단일 연결 리만 곡면이 열린 단위 원판이나 복소평면, 리만 구 가운데 하나로 전단사 이 존재한다는 정리다.
  • 数学上,曲面的单值化定理是说任何曲面上都有一个常高斯曲率的度量。事实上,在每一个给定的中我们都可以找到一个常高斯曲率的度量。等价的說,用复分析的语言,任何单连通的黎曼曲面都共形等价於复平面、单位圆盘和黎曼球面三者之一。
  • In mathematics, the uniformization theorem says that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere. In particular it implies that every Riemann surface admits a Riemannian metric of constant curvature. For compact Riemann surfaces, those with universal cover the unit disk are precisely the hyperbolic surfaces of genus greater than 1, all with non-abelian fundamental group; those with universal cover the complex plane are the Riemann surfaces of genus 1, namely the complex tori or elliptic curves with fundamental group Z2; and those with universal cover the Riemann sphere are those of genus zero, namely the Riemann sphere itself, with trivial fundamental group.
  • In de riemann-meetkunde, een deelgebied van de wiskunde, zegt de uniformeringsstelling dat elk enkelvoudig samenhangende riemann-oppervlak hoekgetrouw equivalent is aan een van de drie domeinen: de open eenheidsschijf, het complexe vlak of de riemann-sfeer. In het bijzonder staat het een riemann-metriek met constante kromming toe. Dit classificeert riemann-oppervlakken als elliptisch (positief gekromd - of beter een constante positieve metriek toelatend), parabolisch (vlak) of hyperbolisch (negatief gekromd) op basis van hun universele overdekking.
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