C.I.M.E. Foundation Subseries

3 primary works

Transcendental Methods in Algebraic Geometry

by Jean-Pierre Demailly, Thomas Peternell, Gang Tian, and Andrej N. Tyurin

Published 13 December 1996

Pluripotential Theory

by Giorgio Patrizio, Zbigniew Blocki, Francois Berteloot, and Jean-Pierre Demailly

Published 29 May 2013

Pluripotential theory is a very powerful tool in geometry, complex analysis and dynamics. This volume brings together the lectures held at the 2011 CIME session on "pluripotential theory" in Cetraro, Italy. This CIME course focused on complex Monge-Ampére equations, applications of pluripotential theory to Kahler geometry and algebraic geometry and to holomorphic dynamics. The contributions provide an extensive description of the theory and its very recent developments, starting from basic introductory materials and concluding with open questions in current research.

Ricci Flow and Geometric Applications

by Michel Boileau, Gerard Besson, Carlo Sinestrari, and Gang Tian

Published 11 September 2016

Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. 

The book’s four chapters are based on lectures given by leading researchers in the field of geometric analysis and low-dimensional geometry/topology, respectively offering an introduction to: the differentiable sphere theorem (G. Besson), the geometrization of 3-manifolds (M. Boileau), the singularities of 3-dimensional Ricci flows (C. Sinestrari), and Kähler–Ricci flow (G. Tian). The lectures will be particularly valuable to young researchers interested in differential manifolds.