Extremal Problems in Minkowski Space related to Minimal Networks
| dc.creator | Swanepoel, Konrad J | |
| dc.date | 2007-07-20 | |
| dc.date.accessioned | 2026-07-07T08:19:24Z | |
| dc.date.available | 2026-07-07T08:19:24Z | |
| dc.description | We solve the following problem of Z. Füredi, J. C. Lagarias and F. Morgan [FLM]: Is there an upper bound polynomial in $n$ for the largest cardinality of a set S of unit vectors in an n-dimensional Minkowski space (or Banach space) such that the sum of any subset has norm less than 1? We prove that |S|\leq 2n and that equality holds iff the space is linearly isometric to \ell^n_\infty, the space with an n-cube as unit ball. We also remark on similar questions raised in [FLM] that arose out of the study of singularities in length-minimizing networks in Minkowski spaces. | |
| dc.description | 6 pages. 11-year old paper. Implicit question in the last sentence has been answered in Discrete & Computational Geometry 21 (1999) 437-447 | |
| dc.identifier | https://arxiv.org/abs/0707.3052 | |
| dc.identifier | http://arxiv.org/abs/0707.3052 | |
| dc.identifier | Proceedings of the American Mathematical Society 124 (1996) 2513-2518 | |
| dc.identifier | doi:10.1090/S0002-9939-96-03370-9 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134747 | |
| dc.subject | Metric Geometry | |
| dc.subject | Functional Analysis | |
| dc.subject | 52A40 (Primary) 52A21, 49Q10 (Secondary) | |
| dc.title | Extremal Problems in Minkowski Space related to Minimal Networks | |
| dc.type | text |