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From the reviews:
“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)The Ricci Flow in Riemannian Geometry
A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem
von Ben Andrews und Christopher HopperThis book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.
