Geometric Flows, Volume 12

Geometric flows are non-linear parabolic differential equations which describe the evolution of geometric structures. Inspired by Hamiltons Ricci flow, the field of geometric flows has seen tremendous progress in the past 25 years and yields important applications to geometry, topology, physics, nonlinear analysis, and so on. Of course, the most spectacular development is Hamiltons theory of Ricci flow and its application to three-manifold topology, including the Hamilton-Perelman proof of the Poincar conjecture. This twelfth volume of the annual Surveys in Differential Geometry examines recent developments on a number of geometric flows and related subjects, such as Hamiltons Ricci flow, formation of singularities in the mean curvature flow, the Khler-Ricci flow, and Yaus uniformization conjecture.