| Lectures on the Ricci Flow Contributor(s): Topping, Peter (Author) |
|
 |
ISBN: 0521689473 ISBN-13: 9780521689472 Publisher: Cambridge University Press OUR PRICE: $62.69 Product Type: Paperback - Other Formats Published: October 2006 Annotation: Hamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincar?? conjecture and Thurston's geometrization conjecture. This book gives a concise introduction to the subject with the hindsight of Perelman's breakthroughs from 2002/2003. After describing the basic properties of, and intuition behind the Ricci flow, core elements of the theory are discussed such as consequences of various forms of maximum principle, issues related to existence theory, and basic properties of singularities in the flow. A detailed exposition of Perelman's entropy functionals is combined with a description of Cheeger-Gromov-Hamilton compactness of manifolds and flows to show how a 'tangent' flow can be extracted from a singular Ricci flow. Finally, all these threads are pulled together to give a modern proof of Hamilton's theorem that a closed three-dimensional manifold which carries a metric of positive Ricci curvature is a spherical space form. |
| Additional Information |
| BISAC Categories: - Mathematics | Applied - Mathematics | Topology - General |
| Dewey: 516.362 |
| Series: London Mathematical Society Lecture Notes |
| Physical Information: 0.28" H x 6.02" W x 9.06" (0.43 lbs) 124 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Hamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincar conjecture and Thurston's geometrization conjecture. This book gives a concise introduction to the subject with the hindsight of Perelman's breakthroughs from 2002/2003. After describing the basic properties of, and intuition behind the Ricci flow, core elements of the theory are discussed such as consequences of various forms of maximum principle, issues related to existence theory, and basic properties of singularities in the flow. A detailed exposition of Perelman's entropy functionals is combined with a description of Cheeger-Gromov-Hamilton compactness of manifolds and flows to show how a 'tangent' flow can be extracted from a singular Ricci flow. Finally, all these threads are pulled together to give a modern proof of Hamilton's theorem that a closed three-dimensional manifold which carries a metric of positive Ricci curvature is a spherical space form. |
Contributor Bio(s): Topping, Peter: - Peter Topping is a Senior Lecturer in Mathematics at the University of Warwick. |
