TY - BOOK
AU - Boucksom, Sebastien.
AU - Eyssidieux, Philippe.
AU - Guedj, Vincent.
ED - SpringerLink (Online service)
TI - An Introduction to the Kähler-Ricci Flow
T2 - Lecture Notes in Mathematics,
SN - 9783319008
AV - QA331.7
U1 - 515.94 23
PY - 2013///
CY - Cham
PB - Springer International Publishing, Imprint: Springer
KW - Mathematics
KW - Differential equations, partial
KW - Global differential geometry
KW - Several Complex Variables and Analytic Spaces
KW - Partial Differential Equations
KW - Differential Geometry
N1 - 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
N2 - 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 KÃ¤hler-Ricci flow and its current state-of-the-art. While several excellent books on KÃ¤hler-Einstein geometry are available, there have been no such works on the KÃ¤hler-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. Â The Ricci flow was first introduced by R. Hamilton in the early 1980s, and is central in G. Perelmanâ€™s celebrated proof of the PoincarÃ© conjecture. When specialized for KÃ¤hler manifolds, it becomes the KÃ¤hler-Ricci flow, and reduces to a scalar PDE (parabolic complex Monge-AmpÃ¨re equation). As a spin-off of his breakthrough, G. Perelman proved the convergence of the KÃ¤hler-Ricci flow on KÃ¤hler-Einstein manifolds of positive scalar curvature (Fano manifolds). Shortly after, G. Tian and J. Song discovered a complex analogue of Perelmanâ€™s ideas: the KÃ¤hler-Ricci flow is a metric embodiment of the Minimal Model Program of the underlying manifold, and flips and divisorial contractions assume the role of Perelmanâ€™s surgeries
UR - http://dx.doi.org/10.1007/978-3-319-00819-6
ER -