LEADER 04072nam 22006615 450 001 9910437868503321 005 20200705041647.0 010 $a3-319-00819-6 024 7 $a10.1007/978-3-319-00819-6 035 $a(CKB)3710000000024329 035 $a(SSID)ssj0001049495 035 $a(PQKBManifestationID)11588419 035 $a(PQKBTitleCode)TC0001049495 035 $a(PQKBWorkID)11019463 035 $a(PQKB)11241217 035 $a(DE-He213)978-3-319-00819-6 035 $a(MiAaPQ)EBC3107039 035 $a(PPN)176103414 035 $a(EXLCZ)993710000000024329 100 $a20131001d2013 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 13$aAn Introduction to the Kähler-Ricci Flow /$fedited by Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj 205 $a1st ed. 2013. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2013. 215 $a1 online resource (VIII, 333 p. 10 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2086 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-00818-8 327 $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. 330 $aThis volume collects lecture notes from courses offered at several conferences and workshops, and provides the first exposition in book form of the basic theory of the Kähler-Ricci flow and its current state-of-the-art. While several excellent books on Kähler-Einstein geometry are available, there have been no such works on the Kähler-Ricci flow. The book will serve as a valuable resource for graduate students and researchers in complex differential geometry, complex algebraic geometry and Riemannian geometry, and will hopefully foster further developments in this fascinating area of research.   The Ricci flow was first introduced by R. Hamilton in the early 1980s, and is central in G. Perelman?s celebrated proof of the Poincaré conjecture. When specialized for Kähler manifolds, it becomes the Kähler-Ricci flow, and reduces to a scalar PDE (parabolic complex Monge-Ampère equation). As a spin-off of his breakthrough, G. Perelman proved the convergence of the Kähler-Ricci flow on Kähler-Einstein manifolds of positive scalar curvature (Fano manifolds). Shortly after, G. Tian and J. Song discovered a complex analogue of Perelman?s ideas: the Kähler-Ricci flow is a metric embodiment of the Minimal Model Program of the underlying manifold, and flips and divisorial contractions assume the role of Perelman?s surgeries. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2086 606 $aFunctions of complex variables 606 $aDifferential equations, Partial 606 $aGeometry, Differential 606 $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 615 0$aFunctions of complex variables. 615 0$aDifferential equations, Partial. 615 0$aGeometry, Differential. 615 14$aSeveral Complex Variables and Analytic Spaces. 615 24$aPartial Differential Equations. 615 24$aDifferential Geometry. 676 $a516.36 702 $aBoucksom$b Sebastien$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aEyssidieux$b Philippe$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aGuedj$b Vincent$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437868503321 996 $aIntroduction to the Kähler-Ricci flow$9258667 997 $aUNINA