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

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 e-book type of the elemental conception of the Kähler-Ricci movement and its present cutting-edge. whereas numerous first-class books on Kähler-Einstein geometry can be found, there were no such works at the Kähler-Ricci move. The e-book will function a helpful source for graduate scholars and researchers in advanced differential geometry, complicated algebraic geometry and Riemannian geometry, and should optimistically foster extra advancements during this attention-grabbing quarter of research.
 
The Ricci movement was once first brought via R. Hamilton within the early Nineteen Eighties, and is principal in G. Perelman’s celebrated facts of the Poincaré conjecture. while really expert for Kähler manifolds, it turns into the Kähler-Ricci move, and decreases to a scalar PDE (parabolic advanced Monge-Ampère equation).
As a spin-off of his leap 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 found a fancy analogue of Perelman’s principles: the Kähler-Ricci movement is a metric embodiment of the minimum version software of the underlying manifold, and flips and divisorial contractions imagine the function of Perelman’s surgeries.

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