This book gives a presentation of topics in Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject. The authors have aimed at presenting technical material in a clear and detailed manner. In this volume, geometric aspects of the theory have been emphasized. The book presents the theory of Ricci solitons, Kähler-Ricci flow, compactness theorems, Perelman's entropy monotonicity and no local collapsing, Perelman's reduced distance function and applications to ancient solutions, and a primer of 3-manifold topology. Various technical aspects of Ricci flow have been explained in a clear and detailed manner. The authors have tried to make some advanced material accessible to graduate students and nonexperts. The book gives a rigorous introduction to Perelman's work and explains technical aspects of Ricci flow useful for singularity analysis. Throughout, there are appropriate references so that the reader may further pursue the statements and proofs of the various results.

Readership

Graduate students and research mathematicians interested in geometric analysis, specifically, the use of Ricci flow to study the geometry and topology of three-dimensional manifolds and Perelman's methods for proving the Poincaré conjecture.

Reviews

"...this book is presented in a readable style, with notes and commentary concluding each chapter aiding its readability..."

-- James McCoy for Mathematical Reviews

"The book is meant to be a text book as well as a reference book and it includes exercises as well as the solutions for some of them. In the first part of this volume the authors took great care in making this a self contained book which compiling a great amount of facts related to the Ricci flow, organizing the information in a very clear way giving very often information on the content of each chapter and relating it to other parts of the book."

-- Zentralblatt MATH