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portada Lectures on the Ricci Flow Paperback (London Mathematical Society Lecture Note Series)
Type
Physical Book
Publisher
Author
Year
2006
Language
English
Pages
124
Format
Paperback
ISBN
0521689473
ISBN13
9780521689472
Edition No.
1
Categories

Lectures on the Ricci Flow Paperback (London Mathematical Society Lecture Note Series)

Peter Topping (Author) · Cambridge University Press · Paperback

Lectures on the Ricci Flow Paperback (London Mathematical Society Lecture Note Series) - Peter Topping

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Synopsis "Lectures on the Ricci Flow Paperback (London Mathematical Society Lecture Note Series) "

Hamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincaré 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.

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