Lectures on the Ricci flow [EBook] / Peter Topping.
Lectures on the Ricci flow [EBook] / Peter Topping.
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...
Personal Name(s):  Topping, Peter, (author) 

Imprint: 
Cambridge :
Cambridge University Press,
2006

Physical Description: 
1 online resource (x, 113 pages) 
Note: 
englisch 
ISBN: 
9780511721465 9780521689472 
Series Title: 
London Mathematical Society lecture note series ;
325 
Subject (LOC):  
Full Text 
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 CheegerGromovHamilton 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 threedimensional manifold whichcarries a metric of positive Ricci curvature is a spherical space form. 