佩雷尔曼 庞加莱猜想3

佩雷尔曼 庞加莱猜想3

ID:15414696

大小:121.02 KB

页数:7页

时间:2018-08-03

佩雷尔曼 庞加莱猜想3_第1页
佩雷尔曼 庞加莱猜想3_第2页
佩雷尔曼 庞加莱猜想3_第3页
佩雷尔曼 庞加莱猜想3_第4页
佩雷尔曼 庞加莱猜想3_第5页
资源描述:

《佩雷尔曼 庞加莱猜想3》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、FiniteextinctiontimeforthesolutionstotheRicciflowoncertainthree-manifoldsGrishaPerelman∗February1,2008InourpreviouspaperweconstructedcompletesolutionstotheRicciflowwithsurgeryforarbitraryinitialriemannianmetricona(closed,oriented)three-manifold[P,6.1],andusedthebehavior

2、ofsuchsolutionstoclassifythree-manifoldsintothreetypes[P,8.2].Inparticular,thefirsttypeconsistedofthosemanifolds,whoseprimefactorsarediffeomorphiccopiesofsphericalspaceformsandS2×S1;theywerecharacterizedbythepropertythattheyadmitmetrics,thatgiverisetosolutionstotheRicci

3、flowwithsurgery,whichbecomeextinctinfinitetime.Whilethisclassificationwassufficienttoanswertopologicalques-tions,ananalyticalquestionofsignificantindependentinterestremainedopen,namely,whetherthesolutionbecomesextinctinfinitetimeforeveryinitialmetriconamanifoldofthistype.Int

4、hisnoteweprovethatthisisindeedthecase.Ourargument(incon-junctionwith[P,§1-5])alsogivesadirectproofofthesocalled”elliptizationconjecture”.Itturnsoutthatitdoesnotrequireanysubstantiallynewideas:weuseonlyaversionoftheleastareadiskargumentfrom[H,§11]andaregu-larizationoft

5、hecurveshorteningflowfrom[A-G].1Finitetimeextinction1.1Theorem.LetMbeaclosedorientedthree-manifold,whoseprimedecom-positioncontainsnoasphericalfactors.ThenforanyinitialmetriconMthesolutiontotheRicciflowwithsurgerybecomesextinctinfinitetime.arXiv:math/0307245v1[math.DG]17

6、Jul2003ProofforirreducibleM.LetΛMdenotethespaceofallcontractibleloopsinC1(S1→M).GivenariemannianmetricgonMandc∈ΛM,defineA(c,g)tobetheinfimumoftheareasofalllipschitzmapsfromD2toM,whoserestrictionto∂D2=S1isc.ForafamilyΓ⊂ΛMletA(Γ,g)bethesupremumofA(c,g)overallc∈Γ.Finally,f

7、oranontrivialhomotopyclassα∈π∗(ΛM,M)letA(α,g)betheinfimumofA(Γ,g)overallΓ∈α.SinceMisnotaspherical,itfollowsfromaclassical(andelementary)resultofSerrethatsuchanontrivialhomotopyclassexists.∗St.PetersburgbranchofSteklovMathematicalInstitute,Fontanka27,St.Petersburg191023

8、,Russia.Email:perelman@pdmi.ras.ruorperelman@math.sunysb.edu11.2Lemma.(cf.[H,§11])IfgtisasmoothsolutiontotheRicciflow,thenfor

当前文档最多预览五页,下载文档查看全文

此文档下载收益归作者所有

当前文档最多预览五页,下载文档查看全文
温馨提示:
1. 部分包含数学公式或PPT动画的文件,查看预览时可能会显示错乱或异常,文件下载后无此问题,请放心下载。
2. 本文档由用户上传,版权归属用户,天天文库负责整理代发布。如果您对本文档版权有争议请及时联系客服。
3. 下载前请仔细阅读文档内容,确认文档内容符合您的需求后进行下载,若出现内容与标题不符可向本站投诉处理。
4. 下载文档时可能由于网络波动等原因无法下载或下载错误,付费完成后未能成功下载的用户请联系客服处理。