QUASI CONFORMAL GEOMETRY AND MOSTOW RIGIDITY
15 Pages
English
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QUASI CONFORMAL GEOMETRY AND MOSTOW RIGIDITY

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15 Pages
English

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QUASI-CONFORMAL GEOMETRY AND MOSTOW RIGIDITY by Marc BOURDON Abstract. — We present the basic tools and results of quasi-conformal geometry of Euclidean spheres. We use them to prove the Mostow rigid- ity theorem and the Sullivan-Tukia theorem, for the real hyperbolic spaces. Resume (Geometrie quasi-conforme et rigidite de Mostow) On presente les resultats et outils standards de la geometrie quasi- conforme des spheres euclidiennes. On les utilise ensuite pour demontrer les theoremes de rigidite de Mostow et de Sullivan-Tukia, dans le cas des espaces hyperboliques reels. Contents 1. Quasi-conformal geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2. Quasi-isometries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3. Mostow rigidity (proof). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4. Sullivan-Tukia's theorem (proof) . . . . . . . . . . . . . . . . . . . . 10 References.

  • ?x? y??·

  • mostow

  • theoremes de rigidite de mostow et de sullivan-tukia

  • then there

  • mobius homeomorphisms

  • curve ? joining

  • let b1


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QUASI-CONFORMALGEOMETRYANDMOSTOWRIGIDITYybMarcBOURDONAbstract.—Wepresentthebasictoolsandresultsofquasi-conformalgeometryofEuclideanspheres.WeusethemtoprovetheMostowrigid-itytheoremandtheSullivan-Tukiatheorem,fortherealhyperbolicspaces.Re´sume´(Ge´ome´triequasi-conformeetrigidite´deMostow)Onpre´sentelesre´sultatsetoutilsstandardsdelage´ome´triequasi-conformedessphe`reseuclidiennes.Onlesutiliseensuitepourde´montrerlesthe´ore`mesderigidite´deMostowetdeSullivan-Tukia,danslecasdesespaceshyperboliquesre´els.Contents1.Quasi-conformalgeometry............................22.Quasi-isometries.....................................73.Mostowrigidity(proof)..............................94.Sullivan-Tukiastheorem(proof)....................10References..............................................14LetHnbetherealhyperbolicspacewithn3.Theaimoftheselecturesistopresentthebasictoolsofquasi-conformalgeometryofthe2000MathematicsSubjectClassification.—30C65,53C24.Keywordsandphrases.—Quasi-conformalHomeomorphism,HyperbolicGe-ometry,Rigidity.