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- Riemann_mapping_theorem abstract "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 (bijective and holomorphic) mapping f from U onto the open unit disk This mapping is known as a Riemann mapping.Intuitively, the condition that U be simply connected means that U does not contain any “holes”. The fact that f is biholomorphic implies that it is a conformal map and therefore angle-preserving. Intuitively, such a map preserves the shape of any sufficiently small figure, while possibly rotating and scaling (but not reflecting) it.Henri Poincaré proved that the map f is essentially unique: if z0 is an element of U and φ is an arbitrary angle, then there exists precisely one f as above such that f(z0) = 0 and that the argument of the derivative of f at the point z0 is equal to φ. This is an easy consequence of the Schwarz lemma.As a corollary of the theorem, any two simply connected open subsets of the Riemann sphere which both lack at least two points of the sphere can be conformally mapped into each other (because conformal equivalence is an equivalence relation).".
- Riemann_mapping_theorem wikiPageExternalLink Grund.pdf.
- Riemann_mapping_theorem wikiPageExternalLink GrayRMT.pdf.
- Riemann_mapping_theorem wikiPageID "26215".
- Riemann_mapping_theorem wikiPageRevisionID "590948731".
- Riemann_mapping_theorem authorlink "William Fogg Osgood".
- Riemann_mapping_theorem first "E.P.".
- Riemann_mapping_theorem first "William Fogg".
- Riemann_mapping_theorem hasPhotoCollection Riemann_mapping_theorem.
- Riemann_mapping_theorem id "Riemann_theorem".
- Riemann_mapping_theorem last "Dolzhenko".
- Riemann_mapping_theorem last "Osgood".
- Riemann_mapping_theorem title "Riemann theorem".
- Riemann_mapping_theorem year "1900".
- Riemann_mapping_theorem subject Category:Theorems_in_complex_analysis.
- Riemann_mapping_theorem type Abstraction100002137.
- Riemann_mapping_theorem type Communication100033020.
- Riemann_mapping_theorem type Message106598915.
- Riemann_mapping_theorem type Proposition106750804.
- Riemann_mapping_theorem type Statement106722453.
- Riemann_mapping_theorem type Theorem106752293.
- Riemann_mapping_theorem type TheoremsInComplexAnalysis.
- Riemann_mapping_theorem comment "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 (bijective and holomorphic) mapping f from U onto the open unit disk This mapping is known as a Riemann mapping.Intuitively, the condition that U be simply connected means that U does not contain any “holes”.".
- Riemann_mapping_theorem label "Afbeeldingstelling van Riemann".
- Riemann_mapping_theorem label "Riemann mapping theorem".
- Riemann_mapping_theorem label "Riemannscher Abbildungssatz".
- Riemann_mapping_theorem label "Teorema de representación conforme de Riemann".
- Riemann_mapping_theorem label "Teorema della mappa di Riemann".
- Riemann_mapping_theorem label "Théorème de l'application conforme".
- Riemann_mapping_theorem label "Теорема Римана об отображении".
- Riemann_mapping_theorem label "リーマンの写像定理".
- Riemann_mapping_theorem label "黎曼映射定理".
- Riemann_mapping_theorem sameAs Riemannscher_Abbildungssatz.
- Riemann_mapping_theorem sameAs Teorema_de_representación_conforme_de_Riemann.
- Riemann_mapping_theorem sameAs Théorème_de_l'application_conforme.
- Riemann_mapping_theorem sameAs Teorema_della_mappa_di_Riemann.
- Riemann_mapping_theorem sameAs リーマンの写像定理.
- Riemann_mapping_theorem sameAs 리만_사상_정리.
- Riemann_mapping_theorem sameAs Afbeeldingstelling_van_Riemann.
- Riemann_mapping_theorem sameAs m.06jn1.
- Riemann_mapping_theorem sameAs Q927051.
- Riemann_mapping_theorem sameAs Q927051.
- Riemann_mapping_theorem sameAs Riemann_mapping_theorem.
- Riemann_mapping_theorem wasDerivedFrom Riemann_mapping_theorem?oldid=590948731.
- Riemann_mapping_theorem isPrimaryTopicOf Riemann_mapping_theorem.