Lectures on the Ricci flow
These notes represent an updated version of a course on Hamilton’s Ricci flow that I gave at the University of Warwick in the spring of 2004. I have aimed to give an introduction to the main ideas of the subject, a large proportion of which are due to Hamilton over the period since he introduced the Ricci flow in 1982. The main difference between these notes and others which are available at the time of writing is that I follow the quite different route which is natural in the light of work of Perelman from 2002. It is now understood how to ‘blow up’ general Ricci flows near their singularities, as one is used to doing in other contexts within geometric analysis. This technique is now central to the subject and is emphasized throughout. The original lectures were delivered to a mixture of graduate students, postdocs, staff, and even some undergraduates. Generally I assumed that the audience had just completed a first course in differential geometry, and an elementary course in PDE, and were just about to embark on a more advanced course in PDE. I tried to make the lectures accessible to the general mathematician motivated by the applications of the theory to the Poincaré conjecture, and Thurston’s geometrisation conjecture
eBook, English, 2006
Cambridge University Press, Cambridge, 2006