On the existence of completely saturated packings and completely reduced covering
| dc.creator | Bowen, Lewis | |
| dc.date | 2001-10-23 | |
| dc.date.accessioned | 2026-07-07T04:44:02Z | |
| dc.date.available | 2026-07-07T04:44:02Z | |
| dc.description | A packing by a body $K$ is collection of congruent copies of $K$ (in either Euclidean or hyperbolic space) so that no two copies intersect nontrivially in their interiors. A covering by $K$ is a collection of congruent copies of $K$ such that for every point $p$ in the space there is copy in the collection containing $p$. A completely saturated packing is one in which it is not possible to replace a finite number of bodies of the packing with a larger number and still remain a packing. A completely reduced covering is one in which it is not possible to replace a finite number of bodies of the covering with a smaller number and still remain a covering. It was conjectured by G. Fejes Toth, G. Kuperberg, and W. Kuperberg that completely saturated packings and commpletely reduced coverings exist for every body $K$ in either $n$-dimensional Euclidean or $n$-dimensional hyperbolic space. We prove this conjecture. | |
| dc.description | 14 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0110260 | |
| dc.identifier | http://arxiv.org/abs/math/0110260 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62476 | |
| dc.subject | Metric Geometry | |
| dc.subject | 52C17, 52A40, 52C26 | |
| dc.title | On the existence of completely saturated packings and completely reduced covering | |
| dc.type | text |