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Journal Articles Annales Scientifiques de l'École Normale Supérieure Year : 2021

Flag-approximability of convex bodies and volume growth of Hilbert geometries

Abstract

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.
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Dates and versions

hal-01423693 , version 1 (30-12-2016)

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Constantin Vernicos, Cormac Walsh. Flag-approximability of convex bodies and volume growth of Hilbert geometries. Annales Scientifiques de l'École Normale Supérieure, 2021, 54, pp.1297-1315. ⟨10.24033/asens.2482⟩. ⟨hal-01423693⟩
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