An Introduction To The Kahler-ricci Flow by Sebastien BoucksomAn Introduction To The Kahler-ricci Flow by Sebastien Boucksom

An Introduction To The Kahler-ricci Flow

bySebastien BoucksomEditorPhilippe Eyssidieux, Vincent Guedj

Paperback | October 14, 2013

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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 Kähler-Ricci flow and its current state-of-the-art. While several excellent books on Kähler-Einstein geometry are available, there have been no such works on the Kähler-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. Perelman's celebrated proof of the Poincaré conjecture. When specialized for Kähler manifolds, it becomes the Kähler-Ricci flow, and reduces to a scalar PDE (parabolic complex Monge-Ampère equation).
As a spin-off of his breakthrough, G. Perelman proved the convergence of the Kähler-Ricci flow on Kähler-Einstein manifolds of positive scalar curvature (Fano manifolds). Shortly after, G. Tian and J. Song discovered a complex analogue of Perelman's ideas: the Kähler-Ricci flow is a metric embodiment of the Minimal Model Program of the underlying manifold, and flips and divisorial contractions assume the role of Perelman's surgeries.

Title:An Introduction To The Kahler-ricci FlowFormat:PaperbackDimensions:333 pagesPublished:October 14, 2013Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319008188

ISBN - 13:9783319008189


Table of Contents

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

Editorial Reviews

"This volume comprises contributions to a series of meetings centered around the Kähler-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 Kähler-Ricci flow and are a welcome addition to the literature on this topic of great current interest in global analysis." (M. Kunzinger, Monatshefte für Mathematik, 2015)