Vai al contenuto principale della pagina

An Introduction to the Kähler-Ricci Flow [[electronic resource] /] / edited by Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj



(Visualizza in formato marc)    (Visualizza in BIBFRAME)

Titolo: An Introduction to the Kähler-Ricci Flow [[electronic resource] /] / edited by Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj Visualizza cluster
Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2013
Edizione: 1st ed. 2013.
Descrizione fisica: 1 online resource (VIII, 333 p. 10 illus.)
Disciplina: 516.36
Soggetto topico: Functions of complex variables
Partial differential equations
Differential geometry
Several Complex Variables and Analytic Spaces
Partial Differential Equations
Differential Geometry
Persona (resp. second.): BoucksomSebastien
EyssidieuxPhilippe
GuedjVincent
Note generali: Bibliographic Level Mode of Issuance: Monograph
Nota di contenuto: 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.
Sommario/riassunto: 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.
Titolo autorizzato: Introduction to the Kähler-Ricci flow  Visualizza cluster
ISBN: 3-319-00819-6
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 996466643403316
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 2086