A Generalization of the Circumcenter of a Set
| dc.creator | Girolo, Jack E. | |
| dc.date | 2008-11-07 | |
| dc.date.accessioned | 2026-07-07T10:17:02Z | |
| dc.date.available | 2026-07-07T10:17:02Z | |
| dc.description | Let (X, d) be a Cat(k) space and P a bounded subset of X . If k > 0 then it is required that the diameter of P be less than Pi/(4 sqrt(k)) . Let u: P to R be a bounded non-negative function from P to R. The existence of a unique point in X called the barycenter of P relative to u is established. When u=1, the barycenter is simply the circumcenter of P. The barycenter has a number of properties including a scaling, continuity and limit property. Under suitable conditions, the barycenter is a fixed point of an isometry or group of isometries. Barycenters are used to show that a complete Cat(k) space X is an absolute retract if k is less than or equal to 0, and an absolute neighborhood retract if X is complete and of curvature less than or equal to k. | |
| dc.description | 22 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0811.1227 | |
| dc.identifier | http://arxiv.org/abs/0811.1227 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173718 | |
| dc.subject | Metric Geometry | |
| dc.subject | General Topology | |
| dc.subject | 53C23; 54C55; 54E50 | |
| dc.title | A Generalization of the Circumcenter of a Set | |
| dc.type | text |