About: Uniformization theorem

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Uniformization theorem Goto Sponge Distinct Permalink

An Entity of Type : yago:Theorem106752293, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FUniformization_theorem

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. The theorem is a generalization of the Riemann mapping theorem from simply connected open subsets of the plane to arbitrary simply connected Riemann surfaces.

Attributes	Values
rdf:type	Thing yago:WikicatMathematicalTheorems yago:WikicatTheorems yago:WikicatTheoremsInDifferentialGeometry yago:WikicatTheoremsInGeometry yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Théorème d'uniformisation de Riemann (fr) Teorema di uniformizzazione di Riemann (it) 균일화 정리 (ko) 一意化定理 (ja) Uniformeringsstelling (nl) Uniformization theorem (en) Теорема об униформизации (ru) 单值化定理 (zh) Теорема уніформізації (uk)
rdfs:comment	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). (fr) 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. (it) 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。 (ja) 복소해석학에서 균일화 정리(均一化定理, uniformization theorem)는 단일 연결 리만 곡면이 열린 단위 원판이나 복소평면, 리만 구 가운데 하나로 전단사 등각 사상이 존재한다는 정리다. (ko) Теорема об униформизации — обобщение теоремы Римана об отображении на двумерные римановы многообразия. Можно сказать, что теорема даёт наилучшую метрику в данном конформном классе. (ru) Теорема про уніформізацію — узагальнення теореми Рімана про відображення на двовимірні ріманові многовиди. Можна сказати, що теорема дає найкращу метрику в даному конформному класі. (uk) 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。 (zh) 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. The theorem is a generalization of the Riemann mapping theorem from simply connected open subsets of the plane to arbitrary simply connected Riemann surfaces. (en) 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. (nl)
rdfs:seeAlso	Ricci flow Geometrization Planar Riemann surface
foaf:depiction
dcterms:subject	Riemann surfaces Manifolds Theorems in differential geometry
Wikipage page ID	288270 (xsd:integer)
Wikipage revision ID	1066573590 (xsd:integer)
Link from a Wikipage to another Wikipage	Beltrami equation Schwarz alternating method David Hilbert Hodge star operator Paul Koebe Ricci flow Richard S. Hamilton Riemann surface Perron method Radó's theorem (Riemann surfaces) Riemann surfaces Complex plane Mathematische Zeitschrift Elliptic operator Second-countable space Elliptic curve Gauss–Bonnet theorem Geometrization conjecture Green's function Conformal equivalence Constant curvature Liouville's equation Lipman Bers Sobolev space Harmonic Mathematische Annalen Proceedings of the American Mathematical Society Measurable Riemann mapping theorem Acta Mathematica Torus W. V. D. Hodge American Mathematical Society Manifolds Exterior derivative Felix Klein Nicolas Bourbaki Dirichlet's principle Dirichlet problem Discrete group Isometry group Israel Journal of Mathematics Quotient space (topology) Riemannian manifold Riemannian metric Grigori Perelman Group action (mathematics) Harmonic function Harmonic map Hermann Weyl Hilbert space Theorems in differential geometry Isothermal coordinates Hyperbolic space Riemann sphere L. E. J. Brouwer Laplace operator Hodge theory Triangulation (topology) Sphere

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 60 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software