Asymptotic volume in Hilbert Geometries
Metric Geometry
2014-06-04 v1 Differential Geometry
Symplectic Geometry
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.
Cite
@article{arxiv.1207.1142,
title = {Asymptotic volume in Hilbert Geometries},
author = {Constantin Vernicos},
journal= {arXiv preprint arXiv:1207.1142},
year = {2014}
}