03111nam 2200637Ia 450 991048439680332120200520144314.03-642-16286-X10.1007/978-3-642-16286-2(CKB)2670000000056858(SSID)ssj0000450249(PQKBManifestationID)11293682(PQKBTitleCode)TC0000450249(PQKBWorkID)10434315(PQKB)10632645(DE-He213)978-3-642-16286-2(MiAaPQ)EBC3066097(PPN)149899475(EXLCZ)99267000000005685820101224d2010 uy 0engurnn|008mamaatxtccrThe Ricci flow in Riemannian geometry a complete proof of the differentiable 1/4-pinching sphere theorem /by Ben Andrews, Christopher Hopper1st ed. 2011.Heidelberg Springer-Verlag Berlin Heidelberg20101 online resource (XVIII, 302 p. 13 illus., 2 illus. in color.) Lecture notes in mathematics,0075-8434 ;2011Bibliographic Level Mode of Issuance: Monograph3-642-16285-1 Includes bibliographical references and index.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.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.Lecture notes in mathematics (Springer-Verlag) ;2011.Ricci flowGeometry, RiemannianDifferentiable dynamical systemsDifferential equations, PartialGlobal differential geometryRicci flow.Geometry, Riemannian.Differentiable dynamical systems.Differential equations, Partial.Global differential geometry.516.3/62Andrews Ben478952Hopper Christopher510631MiAaPQMiAaPQMiAaPQBOOK9910484396803321The Ricci flow in Riemannian geometry4198142UNINA