An Introduction to the Kähler-Ricci Flow (Lecture Notes in by Sebastien Boucksom,Philippe Eyssidieux,Vincent Guedj PDF

By Sebastien Boucksom,Philippe Eyssidieux,Vincent Guedj

ISBN-10: 3319008188

ISBN-13: 9783319008189

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 elemental thought of the Kähler-Ricci move and its present cutting-edge. whereas a number of very good books on Kähler-Einstein geometry can be found, there were no such works at the Kähler-Ricci movement. The e-book will function a precious source for graduate scholars and researchers in advanced differential geometry, advanced algebraic geometry and Riemannian geometry, and should expectantly foster additional advancements during this attention-grabbing sector of research.
 
The Ricci movement was once first brought by means of R. Hamilton within the early Nineteen Eighties, and is vital in G. Perelman’s celebrated facts of the Poincaré conjecture. while really good for Kähler manifolds, it turns into the Kähler-Ricci circulation, 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 move on Kähler-Einstein manifolds of confident scalar curvature (Fano manifolds). almost immediately after, G. Tian and J. tune 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 imagine 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


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