The Ricci Flow: An Introduction

The Ricci flow is a powerful technique that integrates geometry, topology, and analysis. Intuitively, the idea is to set up a PDE that evolves a metric according to its Ricci curvature. The resulting equation has much in common with the heat equation, which tends to ''flow'' a given function to ever nicer functions. By analogy, the Ricci flow evolves an initial metric into improved metrics. Richard Hamilton began the systematic use of the Ricci flow in the early 1980s and applied it in particular to study 3-manifolds. Grisha Perelman has made recent breakthroughs aimed at completing Hamilton's program. The Ricci flow method is now central to our understanding of the geometry and topology of manifolds. This book is an introduction to that program and to its connection to Thurston's geometrization conjecture. The book is suitable for geometers and others who are interested in the use of geometric analysis to study the structure of manifolds.

This introductory volume is intended for geometers interested in the use of geometric analysis to study the structure of manifolds. It specifically focuses on Hamilton's program to apply the Ricci flow to approach Thurston's Geometrization Conjecture. Chapters give attention to special and limit solutions, short time existence, maximum principles, derivative estimates, singularities and their dilations, and related topics. Annotation © 2004 Book News, Inc., Portland, OR