This volume collects lecture notes from courses offered at several conferences and workshops, and provides the first exposition in book form of the basic theory

The generalized Ricci flow is a geometric evolution equation which has recently emerged from investigations into mathematical physics, Hitchin's generalized geo

An introduction to Ricci flow suitable for graduate students and research mathematicians.

A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for R