關(guān)于單值化和Ricci流的一些結(jié)果.pdf

1、同濟(jì)大學(xué)理學(xué)院博士學(xué)位論文關(guān)于單值化和Ricci流的一些結(jié)果姓名：阮其華申請學(xué)位級別：博士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：陳志華20050318英文摘要AbstractFourproblemswasdiscussedinthisthesisFirstlywestudytheproblemabouttheuniformizationofcompleteK五hlermallifold，andprovethatforanynoncompactcomp

2、leteKShlermanifoldMwithpositiveRiccicurvature，supposeeithertheholomorphicbisectionalcurvatureispositiveandthescalarcurvaturedl=caysquadraticallyonthegeodesicball，orMisnonpambolic鋤dfinitetopologicaltypetheholomorphicbisec

3、tionalcurvatureandJ0Ric“arebothbounded’thenMisbiholomorphictoaquasiprojectivevarietySecondlywestudythegapphenomcnaonthecompletenoncompactlocallyconformallyflatmanifold，andgetthatforanycompletenoncompactlocallyconformally

4、fiatmanifolds，iftheRiecicurvatureisnonnegativethescalarcurvatureisboundedandthemeanvalueofthescalarcurvaturesatisfiesthedecayingcondition：盯sk(zo，s)如=oqogr)，where老‰，s)=面疆；而1而厶(砘。)R(z)dv，冗(z)andvol(B(zo，s))respectivelydeno

5、tethescalarcurvatureandthevolumeofthegeodesicballB(zo，s)withmdiussandcenterXo，thenthemanifoidisflatThirdlywestudytheRicciflowequationonthenoncompactcompleteKi2hlermanifold，andprovethatforanycompletenoncompactK／ihlermanif

6、oldwjnlnonnegativeandboundedholomorphicbisectionalcurvature，thenecessaryandsuffi—cientconditionoftheexistencefortheimmortalsolutionoftheRicciflowisthat：orsk(z，s)ds≤Clog(2r)forsomeconstantsC0，比∈M，r≥0Finallywestudytheunifo

7、rmizationproblemonnoncompactcompleteRiemanuianmanifoldsatisfyingthegeneralSobol“inequalities，andconcludethatforanycompletendimensionalRiemarmianmanifoldwithnonnegativeRiccicurvatureiforleofthegeneralSobolevinequalitiesis

8、satisfied：，|￡≤cIIfll：IIV川：一，vf∈c字(M)，=；了10，；1=；1一i1，1≤9nforsomepositiveconstantC，thenitisdiffeomorphicto艫Withoutanycurvatureassumption，foranycompletendimensionalRiemannianmanifold，iftheSobolevinequalitiesalesatisfied，nam

9、elyitcorrespondsto0=0inthegeneralSobolevinequality，thenthegeodesicballhasthefollowingvolumegrowth，namelylim叢警趔≥(，1，wherethepositiveconstantCdependsonlyonnandqKeyWords：Uniformization，GapphenomenaRicciflowSobolevinequality