An Introduction to the Kähler-Ricci flow Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj, editors

Format:

Book

Contributor:

Boucksom, Sébastien

Eyssidieux, Philippe

Guedj, Vincent

Series:

Lecture notes in mathematics (Springer-Verlag) 2086

Lecture notes in mathematics 1617-9692 2086

Language:

English

Subjects (All):

Kählerian structures.

Ricci flow.

Physical Description:

1 online resource

Place of Publication:

Cham, Switzerland Springer ©2013

Language Note:

English

System Details:

text file PDF

Summary:

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

Contents:

Introduction Sébastien Boucksom and Philippe Eyssidieux An Introduction to Fully Nonlinear Parabolic Equations Cyril Imbert and Luis Silvestre An Introduction to the Kähler-Ricci Flow Jian Song and Ben Weinkove Regularizing Properties of the Kähler-Ricci Flow Sébastien Boucksom and Vincent Guedj The Kähler-Ricci Flow on Fano Manifolds Huai-Dong Cao Convergence of the Kähler-Ricci Flow on a Kähler-Einstein Fano Manifold Vincent Guedj

Notes:

Includes bibliographical references

Online resource; title from PDF title page (SpringerLink, viewed Oct. 7, 2013)

Other Format:

Printed edition:

ISBN:

9783319008196

3319008196

OCLC:

859522979

Access Restriction:

Restricted for use by site license