IUMJ

Title: Asymptotic volume on Hilbert geometries

Authors: Constantin Vernicos

Issue: Volume 62 (2013), Issue 5, 1431-1441

Abstract:

We prove that the metric balls of a Hilbert geometry admit a volume growth which is bigger than a polynomial function with degree equal to their dimension. We also characterise the convex polytopes as those convex sets whose Hilbert geometry has polynomial volume growth of order equal to their dimension.