Oscillations non linéaires des systèmes hyperboliques : méthodes et résultats qualitatifs
Denis Serre (1991)
Annales de l'I.H.P. Analyse non linéaire
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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.