By Sebastien Boucksom,Philippe Eyssidieux,Vincent Guedj
This quantity collects lecture notes from classes provided at numerous meetings and workshops, and offers the 1st exposition in publication type of the elemental conception of the Kähler-Ricci stream and its present state of the art. whereas a number of first-class books on Kähler-Einstein geometry can be found, there were no such works at the Kähler-Ricci movement. The e-book will function a important source for graduate scholars and researchers in complicated differential geometry, advanced algebraic geometry and Riemannian geometry, and may with a bit of luck foster extra advancements during this interesting region of research.
The Ricci stream was once first brought by means of R. Hamilton within the early Eighties, and is imperative in G. Perelman’s celebrated facts of the Poincaré conjecture. whilst 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 step forward, G. Perelman proved the convergence of the Kähler-Ricci stream on Kähler-Einstein manifolds of optimistic scalar curvature (Fano manifolds). almost immediately after, G. Tian and J. track came across a fancy 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 think the function 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