Semi-normes et ensembles convexes dans un espace vectoriel sur un corps valué ultramétrique
Jean-Pierre Carpentier (1964-1965)
Séminaire Choquet. Initiation à l'analyse
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Jean-Pierre Carpentier (1964-1965)
Séminaire Choquet. Initiation à l'analyse
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A. Issoufou Kouada (1994)
RAIRO - Operations Research - Recherche Opérationnelle
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Gérard Letac (1983)
Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications
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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.
Guy Fourt (1972)
Annales scientifiques de l'Université de Clermont. Mathématiques
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Haïm Brezis (1964-1965)
Séminaire Choquet. Initiation à l'analyse
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Michel Talagrand (1974-1975)
Séminaire Choquet. Initiation à l'analyse
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