38 citations · 81 across the 12 of their papers we have counts for
14 papers
Volume growth of Funk geometry and the flags of polytopes
Dmitry Faifman, Constantin Vernicos, Cormac Walsh
We consider the Holmes--Thompson volume of balls in the Funk geometry on the interior of a convex domain. We conjecture that for a fixed radius, this volume is minimized when the d…
Flag-approximability of convex bodies and volume growth of Hilbert geometries
Constantin Vernicos, Cormac Walsh
We introduce the flag-approximability of a convex body to measure how easy it is to approximate by polytopes. We show that the flag-approximability is exactly half the volume entro…
On the Hilbert Geometry of Convex Polytopes
Constantin Vernicos
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 the…
Asymptotic volume in Hilbert Geometries
Constantin Vernicos
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…
Approximability of convex bodies and volume entropy in Hilbert geometry
Constantin Vernicos
The approximability of a convex body is a number which measures the difficulty to approximate that body by polytopes. We prove that twice the approximability is equal to the volume…
On the Hilbert Geometry of products
Constantin Vernicos
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 e…