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OverviewFull Product DetailsAuthor: Qi S. Zhang (University of California, Riverside, USA)Publisher: Taylor & Francis Inc Imprint: CRC Press Inc Dimensions: Width: 15.60cm , Height: 2.80cm , Length: 23.40cm Weight: 0.780kg ISBN: 9781439834596ISBN 10: 1439834598 Pages: 432 Publication Date: 02 July 2010 Audience: College/higher education , General/trade , Tertiary & Higher Education , General Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction Sobolev Inequalities in the Euclidean Space Weak derivatives and Sobolev space Wk,p(D), D subset Rn Main imbedding theorem for W01,p(D) Poincare inequality and log Sobolev inequality Best constants and extremals of Sobolev inequalities Basics of Riemann Geometry Riemann manifolds, connections, Riemann metric Second covariant derivatives, curvatures Common differential operators on manifolds Geodesics, exponential maps, injectivity radius etc. Integration and volume comparison Conjugate points, cut-locus, and injectivity radius Bochner-Weitzenbock type formulas Sobolev Inequalities on Manifolds A basic Sobolev inequality Sobolev, log Sobolev inequalities, heat kernel Sobolev inequalities and isoperimetric inequalities Parabolic Harnack inequality Maximum principle for parabolic equations Gradient estimates for the heat equation Basics of Ricci Flow Local existence, uniqueness and basic identities Maximum principles under Ricci flow Qualitative properties of Ricci flow Solitons, ancient solutions, singularity models Perelman's Entropies and Sobolev Inequality Perelman's entropies and their monotonicity (Log) Sobolev inequality under Ricci flow Critical and local Sobolev inequality Harnack inequality for the conjugate heat equation Fundamental solutions of heat type equations Ancient Solutions and Singularity Analysis Preliminaries Heat kernel and solutions Backward limits of solutions Qualitative properties of solutions Singularity analysis of 3-dimensional Ricci flow Sobolev Inequality with Surgeries A brief description of the surgery process Sobolev inequality, little loop conjecture, and surgeries Applications to the Poincare Conjecture Evolution of regions near surgery caps Canonical neighborhood property with surgeries Summary and conclusion Bibliography IndexReviewsIt is clear as vodka that, as Zhang advertises in the Preface, 'the first half of the book is aimed at graduate students and the second half is intended for researchers.' With some good timing, the same reader can start as one and continue as the other. ! a very important contribution to the genre. --MAA Reviews, September 2010 Author InformationQi S. Zhang is a professor of mathematics at the University of California, Riverside. Tab Content 6Author Website:Countries AvailableAll regions |
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