Displaying similar documents to “L'enveloppe locale des perturbations d'une union de plans totalement réels qui se coupent en une droite réelle.”

Convexes hyperboliques et fonctions quasisymétriques

Yves Benoist (2003)

Publications Mathématiques de l'IHÉS

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Every bounded convex open set Ω of is endowed with its Hilbert metric . We give a necessary and sufficient condition, called quasisymmetric convexity, for this metric space to be hyperbolic. As a corollary, when the boundary is real analytic, Ω is always hyperbolic. In dimension 2, this condition is: in affine coordinates, the boundary ∂Ω is locally the graph of a C strictly convex function whose derivative is quasisymmetric.