The Ricci Flow: An Introduction

 ( Book Product ) 

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.

• ISBN bar code 9780821835159 ξ1 registered September 22 2015
  
• Product category is Book

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 authors also provide a Guide for the hurried reader, to help readers wishing to develop, as efficiently as possible, a nontechnical appreciation of the Ricci flow program for 3-manifolds, i.e., the so-called fast track. The book is suitable for geometers and others who are interested in the use of geometric analysis to study the structure of manifolds.

^ Dan Knopf (2015). The Ricci Flow: An Introduction ISBN 9780821835159 (revised Nov 2015)