By Sebastien Boucksom,Philippe Eyssidieux,Vincent Guedj
This quantity collects lecture notes from classes provided at numerous meetings and workshops, and gives the 1st exposition in publication kind of the elemental thought of the Kähler-Ricci stream and its present state of the art. whereas numerous first-class books on Kähler-Einstein geometry can be found, there were no such works at the Kähler-Ricci circulation. The ebook will function a precious source for graduate scholars and researchers in advanced differential geometry, advanced algebraic geometry and Riemannian geometry, and may confidently foster extra advancements during this interesting zone of research.
The Ricci movement used to be first brought through R. Hamilton within the early Nineteen Eighties, and is critical in G. Perelman’s celebrated facts of the Poincaré conjecture. whilst really good for Kähler manifolds, it turns into the Kähler-Ricci circulate, 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 circulation on Kähler-Einstein manifolds of confident scalar curvature (Fano manifolds). almost immediately after, G. Tian and J. tune chanced on a fancy analogue of Perelman’s principles: the Kähler-Ricci move is a metric embodiment of the minimum version software of the underlying manifold, and flips and divisorial contractions think the position 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