The Ricci Flow in Riemannian Geometry
A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem
Published on 25. November 2010
Book
Paperback/Softback
XVIII, 302 pages
978-3-642-16285-5 (ISBN)
Description
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 Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.
Reviews / Votes
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)More details
Series
Edition
2011
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
2 farbige Abbildungen, 11 s/w Abbildungen
XVIII, 302 p. 13 illus., 2 illus. in color.
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
1000 gr
ISBN-13
978-3-642-16285-5 (9783642162855)
DOI
10.1007/978-3-642-16286-2
Schweitzer Classification
Other editions
Additional editions
Ben Andrews | Christopher Hopper
The Ricci Flow in Riemannian Geometry
A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem
E-Book
11/2010
Springer
€69.54
Available for download
Content
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 Böhm and Wilking.- 14 Preserving Positive Isotropic Curvature.- 15 The Final Argument