n維復(fù)雙曲空間上的離散群,穩(wěn)定盆定理與基本域.pdf

1、1申請上海交通大學(xué)理學(xué)碩士學(xué)位論文n維復(fù)雙曲空間上的離散群穩(wěn)定盆定理與基本域維復(fù)雙曲空間上的離散群穩(wěn)定盆定理與基本域DISCRETEGROUPSONnDIMENSIONAlCOMPLEXHYPERBOLICSPACESTABLEBASINTHEMTHEFUNDMENTALDOMAIN碩士生：周寅導(dǎo)師：乃兵（副教授）所在院系：理學(xué)院數(shù)學(xué)系所學(xué)專業(yè)：基礎(chǔ)數(shù)學(xué)研究方向：復(fù)分析及其應(yīng)用上海交通大學(xué)理學(xué)院數(shù)學(xué)系二零一零年三月國家自然科學(xué)基金資助3

2、DISCRETEGROUPSONnDIMENSIONAlCOMPLEXHYPERBOLICSPACESTABLEBASINTHEMTHEFUNDMENTALDOMAINABSTRACTInrecentyearsdiscretegroupsonComplexHyperbolicSpacethefundamentaldomainaresomethingthatmathematiciansathomeabroadhavepaidcloseat

3、tentionon.AsweknowmanypapershavebeenstudiedfPU（21C）wehaveobtainedsomeimptantresults.HowevermanyresultsoftwodimensionalComplexHyperbolicSpacedonotstillholdinhighdimensionwhichismecomplexthantwodimensionalcase.Thispapermai

4、nlystudiesndimensionalComplexHyperbolicgroupsPU(n1C)InthestudyofdiscretegroupstablebasintheemdiscretecriterioninPU(21C)areimptantproblems.BasmajianR.Miner[1]KamiyaJohnR.Parker[8]havealotofimptantachievements.Thispaperdiv

5、idesintothreepartsthefirstpartisthatthestablebasintheemincomplextwodimensionalsituationprovedbyJohn.R.Parker[8]canbeextendedtothestablebasintheemincomplexhighdimensionspacethesecondpartundercertainconditionsonkamiyaJohnR

6、.Parker[54]discretecriterionofthesubgroupofPU(21C)whichcontainsscrewparabolictransfmofdiscretecriterionofwillbegeneralizedtohighdimensionspace.KEYWDS:discretegroupsstablebasintheemfundamentaldomainhyperbolicisometricsscr