The Ricci Flow: An Introduction (Mathematical Surveys and Monographs) by Bennett Chow (PDF)

Description

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”.

User’s Reviews

Editorial Reviews: Review “Well written … topics are well-motivated and presented with clarity and insight … proofs are clear yet detailed so that the material is accessible to a wide audience as well as specialists. Gaps in arguments in the literature are filled in.” —- Zentralblatt MATH

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is quite simply the best book on the Ricci Flow that I have ever encountered. This is the only book on the Ricci Flow that I have ever encountered. I believe that its value to the development and application of geometric analysis for the study of manifolds is incalculable (no pun intended). I must say, I have never seen nicer functions or such improved metrics. I am particularly impressed by by the talents of the second author, Dr. Dan Knopf, as displayed in this fine publication. His commanding grasp of the material, lucid and thought-provoking presentation, and fine expository style are nothing short of breathtaking. I am pleased to recommend this excellent work.

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