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An Introduction to the Kähler-Ricci Flow

Author: Sébastien Boucksom; Philippe Eyssidieux; Vincent Guedj
Publisher: Heidelberg : Springer, cop. 2013.
Series: Lecture notes in mathematics (Internet), 2086.
Edition/Format:   Computer file : Document : EnglishView all editions and formats
Database:WorldCat
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 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  Read more...
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Additional Physical Format: An introduction to the Kähler-Ricci flow [Texte imprimé] / Sébastien Boucksom, Philippe Eyssidieux, Vincent Guedj, editors
Cham (Suisse) : Springer, cop. 2013, cop. 2013
1 vol. (VIII-333 p.). (@Lecture notes in mathematics)
978-3-319-00818-9
(ABES)174478909
Material Type: Document
Document Type: Computer File
All Authors / Contributors: Sébastien Boucksom; Philippe Eyssidieux; Vincent Guedj
ISBN: 9783319008196 3319008196
OCLC Number: 875270391
Notes: Titre provenant de la page de titre du document numérisé.
Numérisation de l'édition de Cham ; Heidelberg ; New York [etc.] : Springer, cop. 2013.
Description: 1 online resource.
Details: Nécessite un lecteur de fichier PDF.
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
Series Title: Lecture notes in mathematics (Internet), 2086.
Responsibility: Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj, editors.

Abstract:

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.

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