On the Hilbert Geometry of products
Differential Geometry
2011-09-02 v1 Metric Geometry
Abstract
We prove that the Hilbert geometry of a product of convex sets is bi-lipschitz equivalent the direct product of their respective Hilbert geometries. We also prove that the volume entropy is additive with respect to product and that amenability of a product is equivalent to the amenability of each terms.
Cite
@article{arxiv.1109.0187,
title = {On the Hilbert Geometry of products},
author = {Constantin Vernicos},
journal= {arXiv preprint arXiv:1109.0187},
year = {2011}
}