04072nam 22006615 450 991043786850332120200705041647.03-319-00819-610.1007/978-3-319-00819-6(CKB)3710000000024329(SSID)ssj0001049495(PQKBManifestationID)11588419(PQKBTitleCode)TC0001049495(PQKBWorkID)11019463(PQKB)11241217(DE-He213)978-3-319-00819-6(MiAaPQ)EBC3107039(PPN)176103414(EXLCZ)99371000000002432920131001d2013 u| 0engurnn|008mamaatxtccrAn Introduction to the Kähler-Ricci Flow /edited by Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj1st ed. 2013.Cham :Springer International Publishing :Imprint: Springer,2013.1 online resource (VIII, 333 p. 10 illus.) Lecture Notes in Mathematics,0075-8434 ;2086Bibliographic Level Mode of Issuance: Monograph3-319-00818-8 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.Lecture Notes in Mathematics,0075-8434 ;2086Functions of complex variablesDifferential equations, PartialGeometry, DifferentialSeveral Complex Variables and Analytic Spaceshttps://scigraph.springernature.com/ontologies/product-market-codes/M12198Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Differential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Functions of complex variables.Differential equations, Partial.Geometry, Differential.Several Complex Variables and Analytic Spaces.Partial Differential Equations.Differential Geometry.516.36Boucksom Sebastienedthttp://id.loc.gov/vocabulary/relators/edtEyssidieux Philippeedthttp://id.loc.gov/vocabulary/relators/edtGuedj Vincentedthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK9910437868503321Introduction to the Kähler-Ricci flow258667UNINA