Displaying similar documents to “Caractérisation des ellipsoïdes par leurs groupes d'automorphismes”

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.

Indice d'un hérisson: étude et applications.

Yves Martínez-Maure (2000)

Publicacions Matemàtiques

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Hedgehogs are a natural generalization of convex bodies of class C+ 2. After recalling some basic facts concerning this generalization, we use the notion of index to study differential and integral geometries of hedgehogs. As applications, we prove a particular case of the Tennis Ball Theorem and a property of normals to a plane convex body of constant width.