On the Hilbert geometry of products

Constantin Vernicos (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We prove that the Hilbert geometry of a product of convex sets is bi-lipschitz equivalent the direct product of their respective Hilbert geometries. We also prove that the volume entropy is additive with respect to product and that amenability of a product is equivalent to the amenability of each terms.

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

Constantin Vernicos. On the Hilbert geometry of products. Proceedings of the American Mathematical Society, 2015, 143 (7), pp.3111-3121. ⟨10.1090/S0002-9939-2015-12504-X⟩. ⟨hal-01160273⟩