An Introduction to the Kähler-Ricci Flow

Nonfiction, Science & Nature, Mathematics, Differential Equations, Mathematical Analysis
Cover of the book An Introduction to the Kähler-Ricci Flow by , Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: ISBN: 9783319008196
Publisher: Springer International Publishing Publication: October 2, 2013
Imprint: Springer Language: English
Author:
ISBN: 9783319008196
Publisher: Springer International Publishing
Publication: October 2, 2013
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Proceedings of China-Europe Conference on Geotechnical Engineering by
Cover of the book Introduction to Annotated Logics by
Cover of the book Inorganic Nanoarchitectures by Organic Self-Assembly by
Cover of the book Modeling and Optimization for Mobile Social Networks by
Cover of the book Dopamine and Sleep by
Cover of the book Transport Phenomena in Newtonian Fluids - A Concise Primer by
Cover of the book Cultures and Contexts of Jewish Education by
Cover of the book Advances in Geometry and Lie Algebras from Supergravity by
Cover of the book Proceedings of the Symposium of Aeronautical and Aerospace Processes, Materials and Industrial Applications by
Cover of the book Modelling Aging and Migration Effects on Spatial Labor Markets by
Cover of the book Harmonic and Complex Analysis in Several Variables by
Cover of the book Advances in Transitional Flow Modeling by
Cover of the book Molecular Machines and Motors by
Cover of the book Equivalent Stress Concept for Limit State Analysis by
Cover of the book Power, Culture and Situated Research Methodology by
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy