An Introduction to the Kähler-Ricci Flow

Sebastien Boucksom

ISBN 10: 3319008188 / ISBN 13: 9783319008189

Verlag: Springer International Publishing, Springer International Publishing Okt 2013, 2013

Beschreibung

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 344 pp. Englisch.

Bestandsnummer des Verkäufers 9783319008189

Bibliografische Details

• Titel: An Introduction to the Kähler-Ricci Flow
• Verlag: Springer International Publishing, Springer International Publishing Okt 2013
• Erscheinungsjahr: 2013
• Sprache: Englisch
• ISBN-10: 3319008188
• ISBN-13: 9783319008189
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 235B x 155 H x 19 T Millimeter Breite: 235 mm, Höhe: 155 mm, Tiefe: 19 mm
• Gewicht: 522 Gramm

Über diesen Titel

Inhaltsangabe

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.