03168nam a22004575i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001200153072001700165072002300182082001500205100003400220245013900254264007500393300004500468336002600513337002600539338003600565347002400601490005300625505019500678520136300873650001702236650003702253650003402290650001702324650005102341650003602392650002702428700003502455700002902490710003402519773002002553776003602573830005302609856004802662978-3-319-00819-6DE-He21320150803155056.0cr nn 008mamaa131001s2013 gw | s |||| 0|eng d a97833190081967 a10.1007/978-3-319-00819-62doi 4aQA331.7 7aPBKD2bicssc 7aMAT0340002bisacsh04a515.942231 aBoucksom, Sebastien.eeditor.13aAn Introduction to the Kähler-Ricci Flowh[electronic resource] /cedited by Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj. 1aCham :bSpringer International Publishing :bImprint: Springer,c2013. aVIII, 333 p. 10 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aLecture Notes in Mathematics,x0075-8434 ;v20860 aThe (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. aThis 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 0aMathematics. 0aDifferential equations, partial. 0aGlobal differential geometry.14aMathematics.24aSeveral Complex Variables and Analytic Spaces.24aPartial Differential Equations.24aDifferential Geometry.1 aEyssidieux, Philippe.eeditor.1 aGuedj, Vincent.eeditor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9783319008189 0aLecture Notes in Mathematics,x0075-8434 ;v208640uhttp://dx.doi.org/10.1007/978-3-319-00819-6