By Sebastien Boucksom,Philippe Eyssidieux,Vincent Guedj

This quantity collects lecture notes from classes provided at a number of meetings and workshops, and gives the 1st exposition in booklet kind of the fundamental conception 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 movement. The booklet will function a priceless source for graduate scholars and researchers in advanced differential geometry, advanced algebraic geometry and Riemannian geometry, and should expectantly foster extra advancements during this interesting region of research.

The Ricci movement used to be first brought by way of R. Hamilton within the early Nineteen Eighties, and is critical in G. Perelman’s celebrated facts of the Poincaré conjecture. whilst really expert for Kähler manifolds, it turns into the Kähler-Ricci movement, and decreases to a scalar PDE (parabolic complicated Monge-Ampère equation).

As a spin-off of his step forward, G. Perelman proved the convergence of the Kähler-Ricci movement on Kähler-Einstein manifolds of confident scalar curvature (Fano manifolds). almost immediately after, G. Tian and J. track found a posh analogue of Perelman’s principles: the Kähler-Ricci circulation 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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