The Ricci Flow : techniques and applications. Part I, Geometric aspects / Bennett Chow [and nine others].

Format:

Book

Author/Creator:

Chow, Bennett, author.

Series:

Mathematical surveys and monographs ; volume 135.

Mathematical surveys and monographs ; volume 135

Language:

English

Subjects (All):

Global differential geometry.

Ricci flow.

Riemannian manifolds.

Physical Description:

1 online resource (562 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2007]

Language Note:

English

Summary:

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, Kahler-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 variou

Contents:

""Contents""; ""Preface""; ""What this book is about""; ""Highlights of Part I""; ""Acknowledgments""; ""Contents of Part I of Volume Two""; ""Chapter 1. Ricci Solitons""; ""1. General solitons and their canonical forms""; ""2. Differentiating the soliton equation � local and global analysis""; ""3. Warped products and 2-dimensional solitons""; ""4. Constructing the Bryant steady soliton""; ""5. Rotationally symmetric expanding solitons""; ""6. Homogeneous expanding solitons""; ""7. When breathers and solitons are Einstein""

""3. Steady and expanding breather solutions revisited""""4. Classical entropy and Perelman's energy""; ""5. Notes and commentary""; ""Chapter 6. Entropy and No Local Collapsing""; ""1. The entropy functional W and its monotonicity""; ""2. The functionals μand v""; ""3. Shrinking breathers are shrinking gradient Ricci solitons""; ""4. Logarithmic Sobolev inequality""; ""5. No finite time local collapsing: A proof of Hamilton's little loop conjecture""; ""6. Improved version of no local collapsing and diameter control""; ""7. Some further calculations related to F and W""

""8. Notes and commentary""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed May 28, 2014).

Other Format:

Print version: Part I, Geometric aspects

ISBN:

1-4704-1362-0