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ID:40087314
大小:981.65 KB
页数:75页
时间:2019-07-20
《Perspectives on Geometric Analysis---丘成桐)》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、PERSPECTIVESONGEOMETRICANALYSISSHING-TUNGYAUThisessaygrewfromatalkIgaveontheoccasionoftheseventiethanniversaryoftheChineseMathematicalSociety.IdedicatethelecturetothememoryofmyteacherS.S.Chernwhohadpassedawayhalfayearbefore(December2004).Duringmygrad
2、uatestudies,Iwasratherfreeinpickingresearchtopics.I[724]workedonfundamentalgroupsofmanifoldswithnon-positivecurvature.Butinthesecondyearofmystudies,Istartedtolookintodifferentialequationsonmanifolds.However,atthattime,Chernwasverymuchinterestedinthewo
3、rkofBottonholomorphicvectorfields.AlsohetoldmethatIshouldworkonRiemannhypothesis.(Weilhadtoldhimthatitwastimeforthehypothesistobesettled.)WhileCherndidnotexpresshisopinionsaboutmyresearchongeometricanalysis,hestartedtoappreciateitafewyearslater.Infact
4、,afterCherngaveacourseonCalabi’sworksonaffinegeometryin1972atBerkeley,S.Y.Chengtoldmeabouttheseinspiringlectures.By1973,ChengandIstartedtoworkonsomeproblemsmentionedinChern’slectures.WedidnotrealizethatthegreatgeometersPogorelov,CalabiandNirenbergwerea
5、lsoworkingonthem.WewereexcitedthatwesolvedsomeoftheconjecturesofCalabionimproperaffinespheres.ButsoonafterwefoundoutthatPogorelov[556]publishedhisresultsrightbeforeusbydifferentarguments.Neverthelessourideasareusefulinhandlingotherproblemsinaffinegeometry
6、,andmyknowledgeaboutMonge-Amp`ereequationsstartedtobroadenintheseyears.Chernwasverypleasedbymywork,especiallyafterI[729]solvedtheproblemofCalabionK¨ahlerEinsteinmetricin1976.IhadbeenatStanford,andChernproposedtotheBerkeleyMathDepartmentthattheyhireme
7、.IvisitedBerkeleyin1977forayearandgaveacourseongeometricanalysiswithemphasisonisometricembedding.ChernnominatedmetogiveaplenarytalkattheInternationalCongressinHelsinki.Thetalk[730]wentwell,butmydecisionnottostayatBerkeleydidnotquitepleasehim.Neverthe
8、lessherecommendedmeforapositiononthefacultyattheInstituteforAdvancedStudy.BeforeIacceptedafacultypositionattheInstitute,Iorganizedaspecialyearongeometryin1979attheInstituteattheinvitationofBorel.Thatwasanexcitingyearbecausemostpeopleingeometricanalys
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