Un Groupe Hyperbolique Est Determine Par Son Bord |
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Authors: | Paulin Frederic |
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Affiliation: | Unité de Mathématiques Pures et Appliquées, Unité Mixte de Recherche 128 du Centre National de la Recherche Scientifique Ecole Normale Supérieure de Lyon, 46 allée d'ltalie, 69364 Lyon Cedex 07, France Email: paulin{at}umpa.ens-lyon.fr |
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Abstract: | We construct on the boundary of a hyperbolic group (in Gromov'ssense) a natural visual measure and a natural crossratio. Weprove that the I-quasiconformal homeomorphisms (in Pansu's sense)between the boundaries of hyperbolic groups are the quasimöbiusmaps (that is, the bijections that almost preserve the crossratios),and that they are the extensions of the quasi-isometries betweenthe groups. We define a barycentre for every probability measureon the boundary without atom, extending the Douady-Earle construction. |
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