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 Unsung Legacies of Educators and Events in African American Education by
Cover of the book The Portrayal and Punishment of Terrorists in Western Media by
Cover of the book The Law of Nations and Britain’s Quest for Naval Security by
Cover of the book Annual Update in Intensive Care and Emergency Medicine 2014 by
Cover of the book Battlefield Acoustics by
Cover of the book Physiological Computing Systems by
Cover of the book Three-Dimensional Design Methodologies for Tree-based FPGA Architecture by
Cover of the book PET/CT in Prostate Cancer by
Cover of the book Algorithms for Computational Biology by
Cover of the book Budapest Building Managers and the Holocaust in Hungary by
Cover of the book The Ontology, Psychology and Axiology of Habits (Habitus) in Medieval Philosophy by
Cover of the book Career Paths in Telemental Health by
Cover of the book Historical Disaster Experiences by
Cover of the book Economy, Business and Uncertainty: New Ideas for a Euro-Mediterranean Industrial Policy by
Cover of the book Computational Science and Its Applications – ICCSA 2017 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