50 citations · 170 across the 16 of their papers we have counts for
11 papers · 1 filter
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…
Firm non-expansive mappings in weak metric spaces
Armando W. Gutiérrez, Cormac Walsh
We introduce the notion of firm non-expansive mapping in weak metric spaces, extending previous work for Banach spaces and certain geodesic spaces. We prove that, for firm non-expa…
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…
Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces
Cormac Walsh
We study the horofunction boundaries of Hilbert and Thompson geometries, and of Banach spaces, in arbitrary dimension. By comparing the boundaries of these spaces, we show that the…
The horofunction boundary and isometry group of the Hilbert geometry
Cormac Walsh
The horofunction boundary is a means of compactifying metric spaces that was introduced by Gromov in the 1970s. We describe explicitly the horofunction boundary of the Hilbert geom…
Gauge-reversing maps on cones, and Hilbert and Thompson isometries
Cormac Walsh
We show that a cone admits a gauge-reversing map if and only if it is a symmetric cone. We use this to prove that every isometry of a Hilbert geometry is a collineation unless the…