资源描述：
《佩雷尔曼 庞加莱猜想2》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、Ricciflowwithsurgeryonthree-manifoldsGrishaPerelman∗February1,2008Thisisatechnicalpaper,whichisacontinuationof[I].Hereweverifymostoftheassertions,madein[I,§13];theexceptionsare(1)thestatementthata3-manifoldwhichcollapseswithlocallowerboundforsectionalcurvature
2、isagraphmanifold-thisisdeferredtoaseparatepaper,astheproofhasnothingtodowiththeRicciflow,and(2)theclaimaboutthelowerboundforthevolumesofthemaximalhornsandthesmoothnessofthesolutionfromsometimeon,whichturnedouttobeunjustified,and,ontheotherhand,irrelevantfortheo
3、therconclusions.TheRicciflowwithsurgerywasconsideredbyHamilton[H5,§4,5];unfortu-nately,hisargument,aswritten,containsanunjustifiedstatement(RMAX=Γ,onpage62,lines7-10fromthebottom),whichIwasunabletofix.Ourapproachissomewhatdifferent,andisaimedateventuallyconstruct
4、ingacanonicalRicciflow,definedonalargestpossiblesubsetofspace-time,-agoal,thathasnotbeenachievedyetinthepresentwork.Forthisreason,weconsidertwoscalebounds:thecutoffradiush,whichistheradiusofthenecks,wherethesurg-eriesareperformed,andthemuchlargerradiusr,suchthat
5、thesolutiononthescaleslessthanrhasstandardgeometry.Thepointistomakeharbitrarilysmallwhilekeepingrboundedawayfromzero.NotationandterminologyB(x,t,r)denotestheopenmetricballofradiusr,withrespecttothemetricattimet,centeredatx.P(x,t,r,△t)denotesaparabolicneighbor
6、hood,thatisthesetofallpointsarXiv:math/0303109v1[math.DG]10Mar2003(x′,t′)withx′∈B(x,t,r)andt′∈[t,t+△t]ort′∈[t+△t,t],dependingonthesignof△t.AballB(x,t,ǫ−1r)iscalledanǫ-neck,if,afterscalingthemetricwithfactorr−2,itisǫ-closetothestandardneckS2×I,withtheproductme
7、tric,whereS2hasconstantscalarcurvatureone,andIhaslength2ǫ−1;hereǫ-closereferstoCNtopology,withN>ǫ−1.AparabolicneighborhoodP(x,t,ǫ−1r,r2)iscalledastrongǫ-neck,if,afterscalingwithfactorr−2,itisǫ-closetotheevolvingstandardneck,whichateach∗St.PetersburgbranchofSt
8、eklovMathematicalInstitute,Fontanka27,St.Petersburg191011,Russia.Email:perelman@pdmi.ras.ruorperelman@math.sunysb.edu1timet′∈[−1,0]haslength2ǫ−1andscalarcurvature(1−t′)−1.AmetriconS2×I,su
