Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2086)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
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)
Editors and Affiliations
Bibliographic Information
Book Title: An Introduction to the Kähler-Ricci Flow
Editors: Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-00819-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2013
Softcover ISBN: 978-3-319-00818-9Published: 14 October 2013
eBook ISBN: 978-3-319-00819-6Published: 02 October 2013
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 333
Number of Illustrations: 10 b/w illustrations
Topics: Several Complex Variables and Analytic Spaces, Partial Differential Equations, Differential Geometry