Abstract.
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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Submitted: December 1995, revised version: July 1996
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Bourdon, M. Immeubles hyperboliques, dimension conforme et rigidité de Mostow. GAFA, Geom. funct. anal. 7, 245–268 (1997). https://doi.org/10.1007/PL00001619
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DOI: https://doi.org/10.1007/PL00001619