Flag-approximability of convex bodies and volume growth of Hilbert geometries
Résumé
We show that the volume entropy of a Hilbert geometry on a convex body is exactly twice the flag-approximability of the body. We then show that both of these quantities are maximized in the case of the Euclidean ball. We also compute explicitly the asymptotic volume of a convex polytope, which allows us to prove that simplices have the least asymptotic volume, as was conjectured by the first author.
Domaines
Géométrie métrique [math.MG]| Origine | Fichiers produits par l'(les) auteur(s) |
|---|