19874.復(fù)變函數(shù)中proper映射幾何理論研究

1、分類號Q12壘!三!學(xué)校代碼!Q三壘2密級學(xué)號201咝10Ⅱ塾復(fù)變函數(shù)中proper映射幾何理論研究StudyonGeometricTheoriesofPropermappingofComplexFunctions研究生姓名：賀偉偉指導(dǎo)教師姓名、職稱：董新漢—塾張學(xué)科專業(yè)：基礎(chǔ)數(shù)學(xué)研究方向：分形幾何與復(fù)分析湖南師范大學(xué)學(xué)位評定委員會辦公室二零一五年五月ABSTRACTPropermappingisanimportantobjectins

2、everalcomplexvariables，Itisorigi—natedfromSteinandRemmert’Sstudyofpropermappingsonthecomplexspaceinthe1950sand1960sAtpresent，ithasbecomearapidlygrowingpopularbranchofmathematicsThepropermappingofonevariableismainlyconsid

3、eredintheRie—mannsurfaceThestudyoftheboundarybehaviourofconformalmappingmainlyconcentratesinthe1970sand1980sInrecentyears，therapiddevelopmentoffrac—talgeometryprovidesnewtools，newmethods，newideasforthestudyofboundarybeha

4、viourofanalyticfunctionsWiththepropermappingsappearmanymathe—maticianspayattentiontotheinterectionofthepropermapping，fractalgeometryandboundarypropertywhichistheoneofthehotspotsofdomesticandforeignscholars，andtheyhadgain

5、edsomeachievementsInonecomplexvariablefunctionareas，wecaneasilyknowtheRiemannmap—pingisaspecialpropermappingwhosedegreeisoneTheroleofRiemannexis—tencetheoremiswell—knownintheonecomplexvariablefunctionareasHowever，theexis

6、tenceofpropermappingofbetweefimulti—connectivityregionshasnotbeenresolvedsatisfactorilyTherefore，thepromotionofRiemannexistencetheoremtothepropermappingisofgreatsignificanceInthisthesis，wemainlystudytheexistenceproblemof

7、ofpropermappingsbetweentwomulti’connectivityregionsTheexistenceofpropermappingbetweenthegeneralmulti—connectedregionisverycomplicated，SOweconsiderthespecialareainthispapeLofcourse，therearealsogeneralconclusions(Forexampl

8、e，thecaseoftwomulti—connectivityregions)Inthefirstchapteofthisthesis，wepresentthebackgroundofthestudy，definitionofpropermapping，andrelatedconclusions，alsointroducethemainconclusionsobtainedbyUSThesecondchapteristOstudyth

9、eexistenceproblemofholomorphicpropermappingforconnectivitynumber≤2ofthedomains，andtheresultsobtainedareperfectThethirdchapterstudytheexistenceproblemofholomorphicpropermappingforconnectivitynumber≥2ofthedomains，wesolvedt