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The Ricci Flow in Riemannian Geometry
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A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem
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Artikel-Nr:
9783642162855
Veröffentl:
2010
Seiten:
302
Autor:
Ben Andrews
Gewicht:
484 g
Format:
234x157x18 mm
Serie:
2011, Lecture Notes in Mathematics
Sprache:
Englisch
Beschreibung:
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.
A self contained presentation of the proof of the differentiable sphere theorem
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