The horofunction boundary of the Hilbert geometry
| dc.creator | Walsh, Cormac | |
| dc.date | 2006-11-29 | |
| dc.date | 2008-03-04 | |
| dc.date.accessioned | 2026-07-07T13:07:24Z | |
| dc.date.available | 2026-07-07T13:07:24Z | |
| dc.description | 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. | |
| dc.description | 24 pages, 2 figures; minor changes, examples added | |
| dc.identifier | https://arxiv.org/abs/math/0611920 | |
| dc.identifier | http://arxiv.org/abs/math/0611920 | |
| dc.identifier | Advances in Geometry, 8 (4) 503-529, 2008 | |
| dc.identifier | doi:10.1515/ADVGEOM.2008.032 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228078 | |
| dc.subject | Metric Geometry | |
| dc.title | The horofunction boundary of the Hilbert geometry | |
| dc.type | text |