QUASI CONFORMAL GEOMETRY AND MOSTOW RIGIDITY

Marc Bourdon

Description

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

Sujets

• Bourdon
• Mostów

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 12
• Langue: English

Extrait

QUASI-CONFORMALGEOMETRYAND MOSTOWRIGIDITY yb MarcBOURDON Abstract .—Wepresentthebasictoolsandresultsofquasi-conformal geometryofEuclideanspheres.WeusethemtoprovetheMostowrigid- itytheoremandtheSullivan-Tukiatheorem,fortherealhyperbolic spaces. Re´sume´ (Ge´ome´triequasi-conformeetrigidite´deMostow) Onpre´sentelesre´sultatsetoutilsstandardsdelage´ome´triequasi- conformedessphe`reseuclidiennes.Onlesutiliseensuitepourde´montrer lesthe´ore`mesderigidite´deMostowetdeSullivan-Tukia,danslecasdes espaceshyperboliquesre´els. Contents 1.Quasi-conformalgeometry............................2 2.Quasi-isometries.....................................7 3.Mostowrigidity(proof)..............................9 4.Sullivan-Tukia’stheorem(proof)....................10 References..............................................14 Let H n betherealhyperbolicspacewithn≥3.Theaimofthese lecturesistopresentthebasictoolsofquasi-conformalgeometryofthe 2000MathematicsSubjectClassification.—30C65,53C24. Keywordsandphrases .—Quasi-conformalHomeomorphism,HyperbolicGe- ometry,Rigidity.