By Sebastien Boucksom,Philippe Eyssidieux,Vincent Guedj
This quantity collects lecture notes from classes provided at a number of meetings and workshops, and offers the 1st exposition in publication kind of the elemental thought of the Kähler-Ricci circulate and its present cutting-edge. whereas numerous very good books on Kähler-Einstein geometry can be found, there were no such works at the Kähler-Ricci stream. The publication will function a precious source for graduate scholars and researchers in advanced differential geometry, advanced algebraic geometry and Riemannian geometry, and may with a bit of luck foster extra advancements during this interesting region of research.
The Ricci movement used to be first brought by means of R. Hamilton within the early Nineteen Eighties, and is relevant in G. Perelman’s celebrated facts of the Poincaré conjecture. whilst really good for Kähler manifolds, it turns into the Kähler-Ricci movement, and decreases to a scalar PDE (parabolic advanced Monge-Ampère equation).
As a spin-off of his step forward, G. Perelman proved the convergence of the Kähler-Ricci move on Kähler-Einstein manifolds of confident scalar curvature (Fano manifolds). presently after, G. Tian and J. music came upon a posh analogue of Perelman’s rules: the Kähler-Ricci stream is a metric embodiment of the minimum version application of the underlying manifold, and flips and divisorial contractions suppose the function of Perelman’s surgeries.
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An Introduction to the Kähler-Ricci Flow (Lecture Notes in Mathematics) by Sebastien Boucksom,Philippe Eyssidieux,Vincent Guedj