The Ricci Flow in Riemannian Geometry
A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem
(Sprache: Englisch)
Focusing on Hamilton's Ricci flow, this volume begins with a detailed discussion of the required aspects of differential geometry. The discussion also includes existence and regularity theory, compactness theorems for Riemannian manifolds, and much more.
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Produktinformationen zu „The Ricci Flow in Riemannian Geometry “
Focusing on Hamilton's Ricci flow, this volume begins with a detailed discussion of the required aspects of differential geometry. The discussion also includes existence and regularity theory, compactness theorems for Riemannian manifolds, and much more.
Klappentext zu „The Ricci Flow in Riemannian Geometry “
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 zu „The Ricci Flow in Riemannian Geometry “
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
Bibliographische Angaben
- Autoren: Ben Andrews , Christopher Hopper
- 2010, XVIII, 302 Seiten, 2 farbige Abbildungen, Masse: 15,6 x 23,8 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3642162851
- ISBN-13: 9783642162855
- Erscheinungsdatum: 25.11.2010
Sprache:
Englisch
Pressezitat
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)
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