Lectures in Contemporary Mathematics 3-Hamilton’s Ricci Flow

Ricci flow is a geometric and analytic evolution equation which we believe is related to physical reality. One of the underlying principles of science is unity. In Ricci flow we see the unity of geometry and analysis. It is also expected to exhibit unity with low-dimensional topology. In this book we emphasize the more geometric and analytic aspects of Ricci flow rather than the topological aspects. We also attempt to convey some of the relations and formal similarities between Ricci flow and other geometric flows such as mean curvature flow and other geometric flows is a two-way street.
The purpose of this book is to give an introduction to the Ricci flow for graduate students and mathematicians interested in working in the subject. We have especially targeted the audience of readers who are novices to the Ricci flow.

【Contents】

Chapter 1 Riemannian Geometry
Chapter 2 Fundamentals of the Ricci Flow Equation
Chapter 3 Closed 3-manifolds with Positive Ricci Curvature
Chapter 4 Ricci Solitons and Special Solutions
Chapter 5 Isoperimetric Estimates and No Local Collapsing
Chapter 6 Preparation for Singularity Analysis
Chapter 7 High-dimensional and Noncompact Ricci Flow
Chapter 8 Singularity Analysis
Chapter 9 Ancient Solutions
Chapter 10 Differential Harnack Estimates
Chapter 11 Space-time Geometry