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＜電子ブック＞
An Introduction to the Kähler-Ricci Flow / edited by Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj
(Lecture Notes in Mathematics. ISSN:16179692 ; 2086)

版	1st ed. 2013.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2013
大きさ	VIII, 333 p. 10 illus : online resource
著者標目	Boucksom, Sebastien editor Eyssidieux, Philippe editor Guedj, Vincent editor SpringerLink (Online service)
件　名	LCSH:Functions of complex variables LCSH:Differential equations LCSH:Geometry, Differential FREE:Several Complex Variables and Analytic Spaces FREE:Differential Equations FREE:Differential Geometry
一般注記	The (real) theory of fully non linear parabolic equations -- The KRF on positive Kodaira dimension Kähler manifolds -- The normalized Kähler-Ricci flow on Fano manifolds -- Bibliography 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 HTTP:URL=https://doi.org/10.1007/978-3-319-00819-6

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