This 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 Bohm and
Wilking and Brendle and Schoen have led to a proof of the
differentiable 1/4-pinching sphere theorem.
General
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