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Cover: 9783642162855 | The Ricci Flow in Riemannian Geometry | Ben Andrews (u. a.) | Buch
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The Ricci Flow in Riemannian Geometry
A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem
Taschenbuch von Ben Andrews (u. a.)
Sprache: Englisch

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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.
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.
Inhaltsverzeichnis
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
Details
Erscheinungsjahr: 2010
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xviii
302 S.
11 s/w Illustr.
2 farbige Illustr.
302 p. 13 illus.
2 illus. in color.
ISBN-13: 9783642162855
ISBN-10: 3642162851
Sprache: Englisch
Herstellernummer: 978-3-642-16285-5
Autor: Andrews, Ben
Hopper, Christopher
Hersteller: Springer
Springer, Berlin
Springer Berlin Heidelberg
Abbildungen: XVIII, 302 p. 13 illus., 2 illus. in color.
Maße: 18 x 157 x 234 mm
Von/Mit: Ben Andrews (u. a.)
Erscheinungsdatum: 25.11.2010
Gewicht: 0,484 kg
Artikel-ID: 107287859
Inhaltsverzeichnis
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
Details
Erscheinungsjahr: 2010
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: xviii
302 S.
11 s/w Illustr.
2 farbige Illustr.
302 p. 13 illus.
2 illus. in color.
ISBN-13: 9783642162855
ISBN-10: 3642162851
Sprache: Englisch
Herstellernummer: 978-3-642-16285-5
Autor: Andrews, Ben
Hopper, Christopher
Hersteller: Springer
Springer, Berlin
Springer Berlin Heidelberg
Abbildungen: XVIII, 302 p. 13 illus., 2 illus. in color.
Maße: 18 x 157 x 234 mm
Von/Mit: Ben Andrews (u. a.)
Erscheinungsdatum: 25.11.2010
Gewicht: 0,484 kg
Artikel-ID: 107287859
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