Editing Low-dimensional topology (section)

===Uniformization theorem===
{{Main|Uniformization theorem}}

In [[mathematics]], the '''uniformization theorem'''  says that every [[simply connected]] [[Riemann surface]] is [[Conformal equivalence|conformally equivalent]] to one of the three domains: the open [[unit disk]], the [[complex plane]], or the [[Riemann sphere]]. In particular it admits a [[Riemannian metric]] of [[constant curvature]]. This classifies Riemannian surfaces as elliptic (positively curved—rather, admitting a constant positively curved metric), parabolic (flat), and hyperbolic (negatively curved) according to their [[universal cover]].

The uniformization theorem is a generalization of the [[Riemann mapping theorem]] from proper simply connected [[open set|open]] [[subset]]s of the plane to arbitrary simply connected Riemann surfaces.