KnowraUniformization theoremLinked fromLinked fromThe 13 pages that link to Uniformization theorem, each with the reason it gives.All 13Related 9Narrower topic 1Compared with 3Hyperbolic geometryRelated: The disk case connects complex analysis to hyperbolic metrics on surfaces.Riemann mapping theoremNarrower topic: It extends the planar classification beyond the proper domains covered by this theorem.Conformal mapRelated: It extends conformal classification from planar domains to Riemann surfaces.Riemann surfaceRelated: It classifies surfaces through their universal covers and underpins much of their function theory.Gauss–Bonnet theoremRelated: Gauss–Bonnet constrains the possible geometries through curvature and topology.Elliptic functionRelated: Its framework explains how tori support meromorphic functions with lattice periodicity.Hyperbolic planeRelated: The disk case equips many complex surfaces with hyperbolic geometry.Ricci flowRelated: Surface Ricci flow gives a geometric route to the uniformization of two-dimensional spaces.Geometric analysisRelated: It shows how an analytic equation can classify two-dimensional geometry.Shing-Tung YauCompared with: Unlike Yau’s higher-dimensional existence theorem, uniformization classifies complex curves through their universal covers.Belyi's theoremCompared with: Uniformization classifies complex analytic surfaces, while Belyi's theorem detects an arithmetic field of definition.Mostow rigidity theoremCompared with: Uniformization classifies conformal structures on surfaces rather than making each surface’s hyperbolic metric unique.Bogomolov–Miyaoka–Yau inequalityRelated: The surface equality case is a higher-dimensional analogue of geometric uniformization.