1、分類號(hào)017451學(xué)校代碼10542密級(jí)學(xué)號(hào)201302100797度量空間中砂一一致域的可去性Theremovabilitypropertyof一一一一，●，●1●●●砂一UnnormdomalnsinmetrlcsDaces碩士生姓名：王葉指導(dǎo)教師姓名、職稱：黃曼子教授學(xué)科專業(yè)：基礎(chǔ)數(shù)學(xué)研究方向：函數(shù)論湖南師范大學(xué)學(xué)位評(píng)定委員會(huì)辦公室二零一六年五月一拳一六午直月ABSTRACTIn1928，GrStzschintroducedthe

2、conceptofquasiconformalmappingwhenhedidsomeresearchonRiemannmappingtheoremonakindofspecialmap—pingsfromsquarestectanglesremainingthevertexesinvariantinR2Quasiconformalmappinghasbecomeanimportantbranchofcomplexanalysisthr

3、oughseveraldecadesofdevelopment，anditisrelevanttoKleingroup，com—plexanalyticdynamicsystemandTeichmullerspaceHowtodescribequasicon—formalmappingthroughspecialdomainsisworththinking，and80theanalyticpropertiesandgeometricpr

4、opertiesofspecialdomainsbecomeveryimportantobjectstostudyincomplexanalysisThispaperisdevotedtostudytheremovabilitypropertiesof砂一uniformdomainsinmetricspacesAnditmakesupofsixchapters，whicharearrangedasfollowsInthefirstcha

5、pter，weintroducethebackgroundandmainresultofthispaper，especiallytheremovabilitypropertiesof41一uniformdomainsInthesecondchapter，somebasicconceptssuchasthedefinitionsofquasi—hyperbolicdistanceandsphereconvexdomainsareprese

6、ntedInthefollowingchapter，toprovethemainresultofthispapersomees—sentiallemmasandtheirproofsareintroducedIntheforthchapter，wediscussthesufficientconditionofthemainresultbysplittingupitintoseveralcasesaccordingtothedistanc

7、efromthepointtotheboundaryInthefifthchapter，thenecessaryconditionofthemainresultisderivedInthelastchapter，inordertoprovethemainlemmaofthispaper，whichislabeledaslemma3110wetrytofindakindofspecialcurves，anddividethemintopi