03619nam 22006495 450 99646651490331620200704193241.03-642-16286-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)99267000000005685820101109d2011 u| 0engurnn|008mamaatxtccrThe Ricci Flow in Riemannian Geometry[electronic resource] A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem /by Ben Andrews, Christopher Hopper1st ed. 2011.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2011.1 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,0075-8434 ;2011Partial differential equationsDifferential geometryGlobal analysis (Mathematics)Manifolds (Mathematics)Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Differential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Global Analysis and Analysis on Manifoldshttps://scigraph.springernature.com/ontologies/product-market-codes/M12082Partial differential equations.Differential geometry.Global analysis (Mathematics).Manifolds (Mathematics).Partial Differential Equations.Differential Geometry.Global Analysis and Analysis on Manifolds.516.3/62Andrews Benauthttp://id.loc.gov/vocabulary/relators/aut478952Hopper Christopherauthttp://id.loc.gov/vocabulary/relators/autBOOK996466514903316The Ricci Flow in Riemannian Geometry2597581UNISA