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 e-book type of the elemental thought of the Kähler-Ricci movement and its present state of the art. whereas a number of very good books on Kähler-Einstein geometry can be found, there were no such works at the Kähler-Ricci circulate. The booklet will function a precious source for graduate scholars and researchers in advanced differential geometry, complicated algebraic geometry and Riemannian geometry, and should expectantly foster additional advancements during this attention-grabbing zone of research.
The Ricci circulation was once first brought via R. Hamilton within the early Nineteen Eighties, and is important in G. Perelman’s celebrated evidence of the Poincaré conjecture. whilst really good for Kähler manifolds, it turns into the Kähler-Ricci stream, and decreases to a scalar PDE (parabolic complicated Monge-Ampère equation).
As a spin-off of his leap forward, G. Perelman proved the convergence of the Kähler-Ricci circulate 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 rules: the Kähler-Ricci move is a metric embodiment of the minimum version software of the underlying manifold, and flips and divisorial contractions suppose the position of Perelman’s surgeries.
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Extra resources for An Introduction to the Kähler-Ricci Flow (Lecture Notes in Mathematics)
An Introduction to the Kähler-Ricci Flow (Lecture Notes in Mathematics) by Sebastien Boucksom,Philippe Eyssidieux,Vincent Guedj