An Introduction to the Kähler-Ricci Flow: 2086 (Lecture Notes in Mathematics) - Tapa blanda

 
9783319008189: An Introduction to the Kähler-Ricci Flow: 2086 (Lecture Notes in Mathematics)
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ISBN 10: 3319008188 ISBN 13: 9783319008189
Editorial: Springer, 2013

Sinopsis

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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De la contraportada

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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Editorial
Springer
Año de publicación
2013
Idioma
Inglés
ISBN 10 
3319008188
ISBN 13 
9783319008189
Encuadernación
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Número de páginas
344
Editor
Boucksom Sebastien, Eyssidieux Philippe, Guedj Vincent
Contacto del fabricante
Springer Nature Customer Service Center GmbH
ProductSafety@springernature.com

Europaplatz 3
Heidelberg
69115
Alemania

Otras ediciones populares con el mismo título

9783319008202: An Introduction to the Kähler-Ricci Flow

Edición Destacada

ISBN 10:  331900820X ISBN 13:  9783319008202
Editorial: Springer, 2013
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