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[意]本尼迪特(Benedetti R.) 著 / 世界图书出版公司 / 2012-08 / 平装
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双曲几何讲义
Oneofthemainthemesofthisbookistheconflictbetweenthe"flexibility'andthe"rigiditypropertiesofthehyperbolicmanifolds:thefirstradicaldifferencearisesbetweenthecaseofdimension2andthecaseofhigherdimensions(asprovedinchaptersBandC),anelementaryfeatureofthusphenomenonbeingthedifferencebetweentheRiemannmappingtheoremandLiouville'stheorem,aspointedoutinchapterA.Thuschapterisratherclementaryandmostofitsmaterialmay'betheobjectofanundergraduatecourse.
Togetherwiththerigiditytheorem,abasictoolforthestudyofhyperbolicmanifoldsisMargulis'lemma,adetailedproofofwhichwegiveinchapterD;asaconsequenceofthisresultinthesamechapterwealsogivearatheraccuratedescription,inalldimensions,ofthethin-thickdecompositionofahyperbolicmanifold(especiallyincaseoffinitevolume).
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