The Ricci Flow in Riemannian Geometry A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem /

• Κύριοι συγγραφείς: Andrews, Ben (Συγγραφέας), Hopper, Christopher (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Σειρά: Lecture Notes in Mathematics, 2011
• Θέματα: Mathematics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Partial differential equations.; Differential geometry.; Partial Differential Equations.; Differential Geometry.; Global Analysis and Analysis on Manifolds.

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...

Πίνακας περιεχομένων:

• 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.