ricci flow in riemannian geometry[ben andrews]

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1、LectureNotesinMathematics2011Editors:J.-M.Morel,CachanF.Takens,GroningenB.Teissier,ParisBenAndrews·ChristopherHopperTheRicciFlowinRiemannianGeometryACompleteProofoftheDifferentiable1/4-PinchingSphereTheorem123BenAndrewsChristopherHopperAustralianNationalU

2、niversityUniversityofOxfordMathematicalSciencesInstituteMathematicalInstituteACT0200AustraliaStGiles’24-29Ben.Andrews@anu.edu.auOX13LBOxfordUnitedKingdomhopper@maths.ox.ac.ukISBN:978-3-642-16285-5e-ISBN:978-3-642-16286-2DOI:10.1007/978-3-642-16286-2Sprin

3、gerHeidelbergDordrechtLondonNewYorkLectureNotesinMathematicsISSNprintedition:0075-8434ISSNelectronicedition:1617-9692MathematicsSubjectClassification(2010):35-XX,53-XX,58-XX©Springer-VerlagBerlinHeidelberg2011Thisworkissubjecttocopyright.Allrightsarereser

4、ved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationorpartsthereofispermittedo

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6、c.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Coverdesign:SPiPublisherServicesPrintedonacid-freepaperSpringerispartofSpringerScience+Busi

7、nessMedia(www.springer.com)Forintheverytorrent,tempest,andasImaysay,whirlwindofyourpassion,youmustacquireandbegetatemperancethatmaygiveitsmoothness.—Shakespeare,Hamlet.PrefaceThereisafamoustheorembyRauch,KlingenbergandBergerwhichstatesthatacompletesimply

8、connectedn-dimensionalRiemannianmanifold,forwhichthesectionalcurvaturesarestrictlybetween1and4,ishomeomorphictoan-sphere.Ithasbeenalongstandingopenconjectureastowhetherornotthe‘homeomorphism’conclusioncouldbestrengthenedto