The Ricci Flow in Riemannian Geometry A Complete 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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Andrews, Ben (Autor), Hopper, Christopher (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011.
Edición:1st ed. 2011.
Colección:Lecture Notes in Mathematics, 2011
Temas:
Differential equations.
Geometry, Differential.
Global analysis (Mathematics).
Manifolds (Mathematics).
Differential Equations.
Differential Geometry.
Global Analysis and Analysis on Manifolds.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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