The horofunction boundary of the Hilbert geometry
Metric Geometry
2009-04-23 v2
Abstract
We investigate the horofunction boundary of the Hilbert geometry defined on an arbitrary finite-dimensional bounded convex domain D. We determine its set of Busemann points, which are those points that are the limits of `almost-geodesics'. In addition, we show that any sequence of points converging to a point in the horofunction boundary also converges in the usual sense to a point in the Euclidean boundary of D. We prove that all horofunctions are Busemann points if and only if the set of extreme sets of the polar of D is closed in the Painleve-Kuratowski topology.
Keywords
Cite
@article{arxiv.math/0611920,
title = {The horofunction boundary of the Hilbert geometry},
author = {Cormac Walsh},
journal= {arXiv preprint arXiv:math/0611920},
year = {2009}
}
Comments
24 pages, 2 figures; minor changes, examples added