On the Hilbert geometry of convex polytopes

Constantin Vernicos (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We survey the Hilbert geometry of convex polytopes. In particular we present two important characterizations of these geometries, the first one in terms of the volume growth of their metric balls, the second one as a metric bilipschitzly equivalent to the Hilbert geometry in the simplex.

Mots clés: Hilbert geometry; Finsler geometry; metric spaces; normed vector spaces; Lipschitz distance

Domaines: Géométrie métrique [math.MG]

Constantin Vernicos. On the Hilbert geometry of convex polytopes. Handbook of Hilbert geometry, 22, pp.111-125, 2014, RMA Lectures in Mathematics and Theoretical Physics, 978-3-03719-147-7. ⟨10.4171/147-1/4⟩. ⟨hal-01519108⟩