Lecture Notes in Mathematics

An Introduction to the Kähler-Ricci Flow

Editors: Boucksom, Sebastien, Eyssidieux, Philippe, Guedj, Vincent (Eds.)

  • An educational and up-to-date reference work on non-linear parabolic partial differential equations
  • The only book currently available on the Kähler-Ricci flow
  • The first book to present a complete proof of Perelman’s estimates for the Kähler-Ricci flow
  • Illustrates the connection between the Kähler-Ricci flow and the Minimal Model Program
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About this book

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.

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)


Table of contents (6 chapters)

  • Introduction

    Boucksom, Sébastien (et al.)

    Pages 1-6

  • An Introduction to Fully Nonlinear Parabolic Equations

    Imbert, Cyril (et al.)

    Pages 7-88

  • An Introduction to the Kähler–Ricci Flow

    Song, Jian (et al.)

    Pages 89-188

  • Regularizing Properties of the Kähler–Ricci Flow

    Boucksom, Sébastien (et al.)

    Pages 189-237

  • The Kähler–Ricci Flow on Fano Manifolds

    Cao, Huai-Dong

    Pages 239-297

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-00819-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-319-00818-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to the Kähler-Ricci Flow
Editors
  • Sebastien Boucksom
  • Philippe Eyssidieux
  • Vincent Guedj
Series Title
Lecture Notes in Mathematics
Series Volume
2086
Copyright
2013
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-00819-6
DOI
10.1007/978-3-319-00819-6
Softcover ISBN
978-3-319-00818-9
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 333
Number of Illustrations and Tables
10 b/w illustrations
Topics