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1、H.M.FarkasI.KraRiemannSurfacesWith2727Figures%Springer-VerlagNewYorkHeidelbergBerlinHershelM.FarkasIrwinKraDepartmentofMathematicsDepartmentofMathematicsTheHebrewUniversityofJerusalemS.U.M.Y.atStonyBrookJerusalemStonyBrook,NY11794IsraelUSAEditorialBoardP.R.HalmosF.W.GehringM
2、anagingEditorUniversityofMichiganIndianaUniversityDepartmentofMathematicsDepartmentofMathematicsAnnArbor,Michigan48104Bloomington,Indiana47401USAUSAC.C.MooreUniversityofCaliforniaDepartmentofMathematicsBerkeley,California94720USAAMSClassification(1980):30Fxx,14H15,20H10Libra
3、ryofCongressCataloginginPublicationDataFarkas,HershelMRiemannsurfaces.(Graduatetextsinmathematics;v.71)Bibliography:p.Includesindex.1.Riemannsurfaces.I.Kra,Irwin,jointauthor.II.Title.III.Series.QA333.F37515'.22379-24385Allrightsreserved.Nopartofthisbookmaybetranslatedorrepro
4、ducedinanyformwithoutwrittenpermissionfromSpringer-Verlag.C1980bySpringer-VerlagNewYorkInc.PrintedintheUnitedStatesofAmerica.987654321ISBN0-387-90465-4Springer-VerlagNewYorkHeidelbergBerlinISBN3-540-90465-4Springer-VerlagBerlinHeidelbergNewYorkToEleanorSaraPrefaceThepresentv
5、olumeistheculminationoftenyears'workseparatelyandjoint-ly.Theideaofwritinfthisbookbeganwithasetofnotesforacoursegivenbyoneoftheauthorsin1970-1971attheHebrewUniversity.Thenoteswererefinedserveraltimesandusedasthebasiccontentofcoursesgivensub-sequentlybyeachoftheauthorsattheSt
6、ateUniversityofNewYorkatStonyBrookandtheHebrewUniversity.InthisbookwepresentthetheoryofRiemannsurfacesanditsmanydif-ferentfacets.Webeginfromthemostelementaryaspectsandtrytobringthereaderuptothefrontierofpresent-dayresearch.Wetreatbothopenandclosedsurfacesinthisbook,butourmai
7、nemphasisisonthecompactcase.Infact,ChaptersIII,V,VI,andVIIdealexclusivelywithcompactsurfaces.ChapterslandIIarepreparatory,andChapterIVdealswithuniformization.AllworksonRiemannsurfacesgobacktothefundamentalresultsofRie-mann,Jacobi,Abel,Weierstrass,etc.Ourbookisnoexception.Ina
8、dditiontoourdebttothesemathematiciansofapreviousera,thepresentworkhasbeenin
