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100   $a20101109d2011      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 14$aThe Ricci Flow in Riemannian Geometry$b[electronic resource] $eA Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem /$fby Ben Andrews, Christopher Hopper
205   $a1st ed. 2011.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2011.
215   $a1 online resource (XVIII, 302 p. 13 illus., 2 illus. in color.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2011
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-16285-1 
320   $aIncludes bibliographical references and index.
327   $a1 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.
330   $aThis book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2011
606   $aPartial differential equations
606   $aDifferential geometry
606   $aGlobal analysis (Mathematics)
606   $aManifolds (Mathematics)
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022
606   $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082
615  0$aPartial differential equations.
615  0$aDifferential geometry.
615  0$aGlobal analysis (Mathematics).
615  0$aManifolds (Mathematics).
615 14$aPartial Differential Equations.
615 24$aDifferential Geometry.
615 24$aGlobal Analysis and Analysis on Manifolds.
676   $a516.3/62
700   $aAndrews$b Ben$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478952
702   $aHopper$b Christopher$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a996466514903316
996   $aThe Ricci Flow in Riemannian Geometry$92597581
997   $aUNISA