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Title An Introduction to the Kahler-Ricci flow / Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj, editors.
Imprint Cham, Switzerland : Springer, 2013.

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Series Lecture notes in mathematics, 1617-9692 ; 2086
Lecture notes in mathematics (Springer-Verlag) ; 2086.
Subject Kählerian structures.
Ricci flow.
Alt Name Boucksom, Sébastien.
Eyssidieux, Philippe.
Guedj, Vincent.
Description 1 online resource (viii, 333 pages) : illustrations.
polychrome rdacc
Contents Introduction / Sebastien Boucksom and Philippe Eyssidieux -- An Introduction to Fully Nonlinear Parabolic Equations / Cyril Imbert and Luis Silvestre -- An Introduction to the Kahler-Ricci Flow / Jian Song and Ben Weinkove -- Regularizing Properties of the Kahler-Ricci Flow / Sebastien Boucksom and Vincent Guedj -- The Kahler-Ricci Flow on Fano Manifolds / Huai-Dong Cao -- Convergence of the Kahler-Ricci Flow on a Kahler-Einstein Fano Manifold / Vincent Guedj.
Bibliography Note Includes bibliographical references.
Summary 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 Kahler-Ricci flow and its current state-of-the-art. While several excellent books on Kahler-Einstein geometry are available, there have been no such works on the Kahler-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 Poincare conjecture. When specialized for Kahler manifolds, it becomes the Kahler-Ricci flow, and reduces to a scalar PDE (parabolic complex Monge-Ampere equation). As a spin-off of his breakthrough, G. Perelman proved the convergence of the Kahler-Ricci flow on Kahler-Einstein manifolds of positive scalar curvature (Fano manifolds). Shortly after, G. Tian and J. Song discovered a complex analogue of Perelman's ideas: the Kahler-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.
Note English.
Online resource; title from PDF title page (SpringerLink, viewed Oct. 7, 2013).
ISBN 9783319008196 (electronic bk.)
3319008196 (electronic bk.)
ISBN/ISSN 10.1007/978-3-319-00819-6
OCLC # 859522979
Additional Format Printed edition: 9783319008189

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