Characterizing hyperbolic spaces and real trees
| dc.creator | Frigerio, Roberto | |
| dc.creator | Sisto, Alessandro | |
| dc.date | 2008-10-08 | |
| dc.date.accessioned | 2026-07-07T10:08:41Z | |
| dc.date.available | 2026-07-07T10:08:41Z | |
| dc.description | Let X be a geodesic metric space. Gromov proved that there exists k>0 such that if every sufficiently large triangle T satisfies the Rips condition with constant k times pr(T), where pr(T) is the perimeter T, then X is hyperbolic. We give an elementary proof of this fact, also giving an estimate for k. We also show that if all the triangles T in X satisfy the Rips condition with constant k times pr(T), then X is a real tree. Moreover, we point out how this characterization of hyperbolicity can be used to improve a result by Bonk, and to provide an easy proof of the (well-known) fact that X is hyperbolic if and only if every asymptotic cone of X is a real tree. | |
| dc.description | 13 pages, 3 figures. Comments are welcome | |
| dc.identifier | https://arxiv.org/abs/0810.1526 | |
| dc.identifier | http://arxiv.org/abs/0810.1526 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171081 | |
| dc.subject | Metric Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 53C23; 20F67 | |
| dc.title | Characterizing hyperbolic spaces and real trees | |
| dc.type | text |