The Ricci Flow in Riemannian Geometry [electronic resource] : A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem / by Ben Andrews, Christopher Hopper.
Tipo de material:
TextoSeries Lecture Notes in Mathematics, 2011Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011Descripción: XVIII, 302 p. 13 illus., 2 illus. in color. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783642162862Trabajos contenidos: SpringerLink (Online service)Tema(s): Mathematics | Global analysis | Differential equations, partial | Global differential geometry | Mathematics | Partial Differential Equations | Differential Geometry | Global Analysis and Analysis on ManifoldsFormatos físicos adicionales: Sin títuloClasificación CDD: 515.353 Clasificación LoC:QA370-380Recursos en línea: de clik aquí para ver el libro electrónico 1 Introduction -- 2 Background Material -- 3 Harmonic Mappings -- 4 Evolution of the Curvature -- 5 Short-Time Existence -- 6 Uhlenbecks 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 Bȵhm and Wilking -- 14 Preserving Positive Isotropic Curvature -- 15 The Final Argument.
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 Bȵhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.
ZDB-2-SMA
ZDB-2-LNM
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