Ricci flow on surfaces

Abstract

In this thesis we discuss the Ricci flow in the simplest setting: on two dimensional Riemannian manifolds. The result central in our discussion of the Ricci flow is the uniformization theorem. This is a result from complex analysis and it classifies Riemann surfaces (complex one-dimensional manifolds). As is turns out a connection exists between this result and the Ricci flow on two dimensional Riemannian manifolds. Actually in a somewhat restricted setting the Ricci flow can be used to give a proof of this theorem. In this thesis we will give a discussion of this proof.