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The Ricci Flow in Riemannian Geometry, 2011 A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem Lecture Notes in Mathematics Series, Vol. 2011

Langue : Anglais

Auteurs :

Couverture de l’ouvrage 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.
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

A self contained presentation of the proof of the differentiable sphere theorem

A presentation of the geometry of vector bundles in a form suitable for geometric PDE

A discussion of the history of the sphere theorem and of future challenges

Includes supplementary material: sn.pub/extras

Date de parution :

Ouvrage de 302 p.

15.5x23.5 cm

Disponible chez l'éditeur (délai d'approvisionnement : 15 jours).

63,29 €

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