Lipschitz Characterisation of convex Polytopal Hilbert Geometries

Constantin Vernicos (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We study Hilbert geometries admitting similar singularities on their boundary to those of a simplex. We show that in an adapted neighborhood of those singularities, two such geometries are bi-lipschitz. As a corollary we prove that the Hilbert Geometry of a convex set is bi-lipschitz equivalent to a normed vector space if and only if the convex is a polytope.

Domaines: Géométrie différentielle [math.DG]; Géométrie métrique [math.MG]

Constantin Vernicos. Lipschitz Characterisation of convex Polytopal Hilbert Geometries. Osaka Journal of Mathematics, 2015, 52 (1), pp.215-235. ⟨hal-01160272⟩