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1、CONFORMALINVARIANTSTOPICSINGEOMETRICFUNCTIONTHEORYLARSV.AHLFORSAMSCHELSEAPUBLISHINGAmericanMathematicalSociety·Providence,RhodeIsland2000MathematicsSubjectClassification.Primary30-02.Foradditionalinformationandupdatesonthisbook,visitwww.ams.org/bookpages/chel-371LibraryofCongressC
2、ataloging-in-PublicationDataAhlfors,LarsV.(LarsValerian),1907-1996.Conformalinvariants:topicsingeometricfunctiontheoryILarsV.Ahlfors.p.cm.Originallypublished:NewYork:McGraw-Hill,1973,inseries:McGraw-Hillseriesinhighermathematics.Includesbibliographicalreferencesandindex.ISBN978-0-
3、8218-5270-5(alk.paper)1.Conformalinvariants.2.Functionsofcomplexvariables.3.Geometricfunctiontheory.4.Riemannsurfaces.I.Title.QA331.A462010515'.9-dc222010035576Copyingandreprinting.Individualreadersofthispublication,andnonprofitlibrariesactingforthem,arepermittedtomakefairuseofthe
4、material,suchastocopyachapterforuseinteachingorresearch.Permissionisgrantedtoquotebriefpassagesfromthispublicationinreviews,providedthecustomaryacknowledgmentofthesourceisgiven.Republication,systematiccopying,ormultiplereproductionofanymaterialinthispublicationispermittedonlyunder
5、licensefromtheAmericanMathematicalSociety.RequestsforsuchpermissionshouldbeaddressedtotheAcquisitionsDepartment,AmericanMathematicalSociety,201CharlesStreet,Providence,RhodeIsland02904-2294USA.Requestscanalsobemadebye-mailtoreprint-permission(!)ams.org.©1973heldbytheLarsV.AhlforsT
6、rustof1993.Allrightsreserved.ReprintedbytheAmericanMathematicalSociety,2010.PrintedintheUnitedStatesofAmerica.@)Thepaperusedinthisbookisacid-freeandfallswithintheguidelinesestablishedtoensurepermanenceanddurability.VisittheAMShomepageathttp://wvw.ams.org/10987654321151413121110Con
7、tentsForewordixPrefacexi1.ApplicationsofSchwarz'slemma11-1.Thenoneuclideanmetric11-2.TheSchwarz-Picktheorem31-3.Convexregions51-4.Angularderivatives71-5.Ultrahyperbolicmetrics121-6.Bloch'stheorem141-7.ThePoincaremetricofaregion161·8.Anelementarylowerbound161-9.ThePicardtheorems192
8、.Capacity232-1.Thetransfinitediam
