正則區(qū)域與單葉性內徑.pdf

1、獨創(chuàng)性聲明本人聲明所呈交的學位論文是本人在導師指導下進行的研究工作及取得的研究成果。據我所知，除了文中特別加以標注和致謝的地方外，論文中不包含其他人已經發(fā)表或撰寫過的研究成果，也不包含為獲得或其他教育機構的學位或證書而使用過的材料。與我一同工作的同志對本研究所做的任何貢獻均已在論文中作了明確的說明并表示謝意。學位論文作者鮐、張簽字日期：少j鄉(xiāng)午2月歹日學位論文版權使用授權書本學位論文作者完全了解江西師范大學研究生院有關保留、使用學位論文

2、的規(guī)定，有權保留并向國家有關部門或機構送交論文的復印件和磁盤，允許論文被查閱和借閱。本人授權江西師范大學研究生院可以將學位論文的全部或部分內容編入有關數據庫進行檢索，可以采用影印、縮印或掃描等復制手段保存、匯編學位論文。(保密的學位論文在解密后適用本授權書)學位論文作者張哆愛簽字日期：如尹7肌日ABSTRACTThepresentdissertationisconcernedwiththeinnerradiusdefinedbytheS

3、chwarzianderivativeorpreSchwarzianderivativeintheplaneTheinnerradiusofunivalenceisrelatedtomanyquestionsinthegeometrictheoryoffunctionandisusedtodescripetheimportantgeometricinvariantofhyperbolicRiemannsurfaceToestimatet

4、heinnerradiusofunivalenceofsomespecialregionsisaninterestingproblemformanyscholars，butitisverydifficulttogettheexplicitvalueofinnerradiusofunivalenceforaplanedomainInthisdissertation，weestimatetheinnerradiusofunivalenced

5、efinedbytheSchwarzianderivativeorpreSchwarzianderivativeChapterI：PrefaceThischapterisdevotedtotheexpositionofthebasictheoryoftheinnerradiusofunivalenceintheplane，aswellasthedevelopmentandtheresearchsituationofthetheoryof

6、theinnerradiusofunivalenceThemainresultsofthisdissertationarebrieflyintroducedinthischapterChapterII：OntheinnerradiusofunivalenceaboutclassesofhyperbolicconvexregionInthischapter，weintroducesomeresultsabouttheinnerradius

7、ofunivalencebySchwarzianderivative，thenstudytheinnerradiusofunivalenceaboutclassesofhyperbolicconvexregion，finallyitisturnedtobeaNeharidiskChapterIII：OntheinnerradiusofunivalencedefinedbythepreSchwarzianderivativeInthisc

8、hapter，makinguseofintegralrepresentationofaconformalmapfromtheunitdisktoaregulateddomain，wediscussthepreSchwarzianderivativeoftheconformalmap，thenobtainsomepropertiesoftheregulateddomain，finallyweobtainanewestimationoflo

9、werboundoftheinnerradiusofunivalencebypreSchwarzianderivativeofaregulateddomainwithconvexcornersChapterⅣ：TheSchwarzianderivativeoftheharmonicmappingsintheplaneInthischapterleth(z)beaconformalmapoftheunitdiskontegulateddo