Abstract
We prove that the metric balls of a Hilbert geometry admit a volume growth at least polynomial of degree their dimension. We also characterise the convex polytopes as those having exactly polynomial volume growth of degree their dimension.
- Title
- Asymptotic volume in Hilbert geometries
- Creators - without role
- Constantin Vernicos - Université de Montpellier, Institut Montpelliérain Alexander Grothendieck - IMAG
- Publication Details
- Indiana University Mathematics Journal, Vol.62(5), pp.1431--1441
- Identifiers
- 9946394709311
- Academic Unit
- Institut Montpelliérain Alexander Grothendieck - IMAG
- Language
- English
- Resource Type
- Journal article
- Local Fields
- hal-01160274