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On utilise l'équivalence due à M. Gromov entre l'hyperbolicité d'un espace métrique
géodésique et le fait que ses cônes asymptotiques sont des arbres réels. Ce résultat
permet tout d'abord de donner une nouvelle preuve du fait que l'inégalité isopérimétrique
sous-quadratique implique l'hyperbolicité. Les avantages de cette preuve sont qu'elle est
très courte et qu'elle utilise une seule propriété de la fonction aire de remplissage des
courbes fermées, l'inégalité du quadrilatère....
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