An Introduction to the Kähler-Ricci Flow

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Beschreibung

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.

Zusammenfassung

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: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2013
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Lecture Notes in Mathematics
Inhalt:	viii 333 S. 10 s/w Illustr. 333 p. 10 illus.
ISBN-13:	9783319008189
ISBN-10:	3319008188
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Redaktion:	Boucksom, Sebastien Guedj, Vincent Eyssidieux, Philippe
Herausgeber:	Sebastien Boucksom/Philippe Eyssidieux/Vincent Guedj
Hersteller:	Springer International Publishing Springer International Publishing AG Lecture Notes in Mathematics
Maße:	235 x 155 x 19 mm
Von/Mit:	Sebastien Boucksom (u. a.)
Erscheinungsdatum:	14.10.2013
Gewicht:	0,522 kg

Artikel-ID: 105637741