An Introduction to the Khler-Ricci Flow [Paperback]

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 of the K?hler-Ricci flow and its current state-of-the-art. While several excellent books on K?hler-Einstein geometry are available, there have been no such works on the K?hler-Ricci flow. The book will serve as a valuable resource for graduate students and researchers in complex differential geometry, complex algebraic geometry and Riemannian geometry, and will hopefully foster further developments in this fascinating area of research.
?
The Ricci flow was first introduced by R. Hamilton in the early 1980s, and is central in G. Perelmans celebrated proof of the Poincar? conjecture. When specialized for K?hler manifolds, it becomes the K?hler-Ricci flow, and reduces to a scalar PDE (parabolic complex Monge-Amp?re equation).
As a spin-off of his breakthrough, G. Perelman proved the convergence of the K?hler-Ricci flow on K?hler-Einstein manifolds of positive scalar curvature (Fano manifolds). Shortly after, G. Tian and J. Song discovered a complex analogue of Perelmans ideas: the K?hler-Ricci flow is a metric embodiment of the Minimal Model Program of the underlying manifold, and flips and divisorial contractions assume the role of Perelmans surgeries.

The (real) theory of fully non linear parabolic equations.- The KRF on positive Kodaira dimension K?hler manifolds.- The normalized K?hler-Ricci flow on Fano manifolds.- Bibliography.

This volume comprises contributions to a series of meetings centered around the K?hler-Ricci flow that took place in Toulouse, Marseille, and Luminy in France, as well as in Marrakech, Morocco in 2010 and 2011. & These contributions cover a wide range of the theory and applications of K?hler-Ricci flow and are a welcome addition to the literature on this topic of great current interest in global analysis. lCi