02488nam a22003138i 4500001001600000003000700016008004100023020001800064020001800082035002000100041000800120082001600128100002800144245005900172264007100231300003700302336002600339337002600365338003600391490005900427500001300486505043900499520102200938650001601960856005501976932003202031596000602063949010502069CR9780511721465UkCbUP100303s2006||||enk o ||1 0|eng|d a9780511721465 a9780521689472 a(Sirsi) a795152 aeng04a516.3622221 aTopping, Peter,eauthor10aLectures on the Ricci flowh[E-Book] /cPeter Topping. 1aCambridge :bCambridge University Press,c2006e(CUP)fCUP20200108 a1 online resource (x, 113 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier aLondon Mathematical Society lecture note series ;v325 aenglisch20gPreface --gIntroduction --tRiemannian geometry background --tThe maximum princople --tComments on existence theory for parabolic PDE --tExistence theory for the Ricci flow --tRicci flow as a gradient flow --tCompactness of Riemannian manifolds and flows --tPerelman's w entropy functional --tCurvature pinching and preserved curvature properties under Ricci flow --tThree-manifolds with positive Ricci curvature, and beyond. aHamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the PoincarĂ© 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 whichcarries a metric of positive Ricci curvature is a spherical space form. 0aRicci flow.40uhttps://doi.org/10.1017/CBO9780511721465zVolltext aCambridgeCore (Order 30059) a1 aXX(795152.1)wAUTOc1i795152-1001lELECTRONICmZBrNsYtE-BOOKu8/1/2020xUNKNOWNzUNKNOWN1ONLINE