Editing Uniformization theorem (section)

===Nonlinear flows===
{{see also|Ricci flow#Relationship to uniformization and geometrization}}

[[Richard S. Hamilton]] showed that the [[Ricci flow|normalized Ricci flow]] on a closed surface uniformizes the metric (i.e., the flow converges to a constant curvature metric).  However, his proof relied on the uniformization theorem. The missing step involved Ricci flow on the 2-sphere: a method for avoiding an appeal to the uniformization theorem (for genus 0) was provided by {{harvtxt|Chen|Lu|Tian|2006}};<ref>{{harvnb|Brendle|2010}}</ref> a short self-contained account of Ricci flow on the 2-sphere was given in {{harvtxt|Andrews|Bryan|2010}}.