20808.關(guān)于多調(diào)和映射一些性質(zhì)的研究

1、分類號—立!絲曼!學(xué)校代碼10542密級學(xué)號201201100099關(guān)于多調(diào)和映射一些性質(zhì)的研究Onthestudiesofcertainpropertiesofpolyharmonicmappings博士生姓名：墮墮垡指導(dǎo)教師姓名、職稱：至垡塑!塾撞學(xué)科專業(yè)：基礎(chǔ)數(shù)學(xué)研究方向：魚塹一堡湖南師范大學(xué)學(xué)位評定委員會辦公室二零一五年五月ABSTRACTA2ptimescontinuouslydifferentiablecomplex—val

2、uedfunctionfinInalnpingQinthecomplexplaneCisapolyharmonicmappingOrpharmonicifitsatisfiesthefollowingpartialdifferentiableequation△”f：=A(ZXp1)，=0whereAdenotestheLaplacian△a2a2面十帝ado—map一2=ziy∈QandPisapositiveintegerEspeei

3、afly：ifP=1(respP=2)，thenfiscalledharvnonic(respbiharrnonic)ThemainailllofthisthesisistOstudythepropertiesofpolyhaImoniemappingsdefinedintheunitdiskD，suchaspartialSllInSconvolutionchar—acterizations，theexistenceofextrenle

4、points，starlikeness：COllvexityLandautypetheoreinthreecircletheorem，LipschitzcontinuityandSOOilThisthesisconsistsoffourchaptersandthearrangementisasfollowsInChapterone7WCprovidethebackgroundonourresearchandthestate—ofOllr

5、mainresultsInChaptertWOweinvestigatethecoefficientestimates：theFekete—Sze95problemandtheclosetoconvexradiiofpartialstunsonaclassofch)se—to—convexharmonicillappingsInChapterthreewediscusstheconvolutioncharaclerizalionsofa

6、classofbihatmonicmappiIlgs日丸o(毋k；盯，n：6)，andthenfindthecoelficicntcllalacteri—zationsandtheextremepointsonitssubclass丁B咒o(機(jī)：盯臼b)InChapterfom’wediscussthepropertiesofpolyharmoniemappingsFirstly，weobtainthecoefficientestima