12932.度量空間中ψ一致域的可去性

1、分類號017451學校代碼10542密級學號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：王葉指導教師姓名、職稱：黃曼子教授學科專業(yè)：基礎數學研究方向：函數論湖南師范大學學位評定委員會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