LEADER 03166nam 2200661Ia 450 001 9910484396803321 005 20200520144314.0 010 $a9783642162862 010 $a364216286X 024 7 $a10.1007/978-3-642-16286-2 035 $a(CKB)2670000000056858 035 $a(SSID)ssj0000450249 035 $a(PQKBManifestationID)11293682 035 $a(PQKBTitleCode)TC0000450249 035 $a(PQKBWorkID)10434315 035 $a(PQKB)10632645 035 $a(DE-He213)978-3-642-16286-2 035 $a(MiAaPQ)EBC3066097 035 $a(PPN)149899475 035 $a(EXLCZ)992670000000056858 100 $a20101224d2010 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe Ricci flow in Riemannian geometry $ea complete proof of the differentiable 1/4-pinching sphere theorem /$fby Ben Andrews, Christopher Hopper 205 $a1st ed. 2011. 210 $aHeidelberg $cSpringer-Verlag Berlin Heidelberg$d2010 215 $a1 online resource (XVIII, 302 p. 13 illus., 2 illus. in color.) 225 1 $aLecture notes in mathematics,$x0075-8434 ;$v2011 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9783642162855 311 08$a3642162851 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 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