The Ricci Flow in Riemannian Geometry

A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem

By: Ben Andrews, Christopher Hopper

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Paperback | 25 November 2010

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322 Pages

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23.39 x 15.6 x 1.7

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1 Introduction.- 2 Background Material.- 3 Harmonic Mappings.- 4 Evolution of the Curvature.- 5 Short-Time Existence.- 6 Uhlenbeck's Trick.- 7 The Weak Maximum Principle.- 8 Regularity and Long-Time Existence.- 9 The Compactness Theorem for Riemannian Manifolds.- 10 The F-Functional and Gradient Flows.- 11 The W-Functional and Local Noncollapsing.- 12 An Algebraic Identity for Curvature Operators.- 13 The Cone Construction of Bohm and Wilking.- 14 Preserving Positive Isotropic Curvature.- 15 The Final Argument

Industry Reviews

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"The book is dedicated almost entirely to the analysis of the Ricci flow, viewed first as a heat type equation hence its consequences, and later from the more recent developments due to Perelman's monotonicity formulas and the blow-up analysis of the flow which was made thus possible. ... is very enjoyable for specialists and non-specialists (of curvature flows) alike." (Alina Stancu, Zentralblatt MATH, Vol. 1214, 2011)

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