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An Introduction to the Kähler-Ricci flow

Auteur : Sébastien Boucksom; Philippe Eyssidieux; Vincent Guedj
Éditeur : Cham, Switzerland : Springer, ©2013.
Collection : Lecture notes in mathematics (Springer-Verlag), 2086.
Édition/format :   Livre électronique : Document : EnglishVoir toutes les éditions et tous les formats
Base de données :WorldCat
Résumé :
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  Lire la suite...
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Genre/forme : Electronic books
Format – détails additionnels : Printed edition:
Type d’ouvrage : Document, Ressource Internet
Format : Internet Resource, Computer File
Tous les auteurs / collaborateurs : Sébastien Boucksom; Philippe Eyssidieux; Vincent Guedj
ISBN : 9783319008196 3319008196
Numéro OCLC : 859522979
Description : 1 online resource (viii, 333 pages) : illustrations.
Contenu : Introduction / Sébastien Boucksom and Philippe Eyssidieux --
An Introduction to Fully Nonlinear Parabolic Equations / Cyril Imbert and Luis Silvestre --
An Introduction to the Kähler-Ricci Flow / Jian Song and Ben Weinkove --
Regularizing Properties of the Kähler-Ricci Flow / Sébastien Boucksom and Vincent Guedj --
The Kähler-Ricci Flow on Fano Manifolds / Huai-Dong Cao --
Convergence of the Kähler-Ricci Flow on a Kähler-Einstein Fano Manifold / Vincent Guedj.
Titre de collection : Lecture notes in mathematics (Springer-Verlag), 2086.
Responsabilité : Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj, editors.
Plus d’informations :

Résumé :

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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"This volume comprises contributions to a series of meetings centered around the Kahler-Ricci flow that took place in Toulouse, Marseille, and Luminy in France, as well as in Marrakech, Morocco in Lire la suite...

 
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