English

On the Hilbert Geometry of Convex Polytopes

Metric Geometry 2014-12-02 v1

Abstract

We survey the Hilbert geometry of convex polytopes. In particular we present two important characterisations of these geometries, the first one in terms of the volume growth of their metric balls, the second one as a bi-lipschitz class of the simplexe's geometry.

Keywords

Cite

@article{arxiv.1406.0733,
  title  = {On the Hilbert Geometry of Convex Polytopes},
  author = {Constantin Vernicos},
  journal= {arXiv preprint arXiv:1406.0733},
  year   = {2014}
}

Comments

To appear in the Handbook on Hilbert geometry edited by G. Besson, A. Papadopoulos and M. Troyanov