Immeubles hyperboliques, dimension conforme et rigidité de Mostow
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We adapt to a family of hyperbolic buildings of dimension two, some geometric quasi-conformal arguments which are classical in the case of rank one non compact symmetric spaces. In particular we compute a numeric quasi-isometric invariant : Pansu's conformal dimension of their boundaries. We also prove that their lattices are Mostow-rigid in the classical sense.
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