Spherical and hyperbolic lengths of images of arcs
| dc.creator | Carne, T. K. | |
| dc.date | 2007-11-01 | |
| dc.date.accessioned | 2026-07-07T08:39:55Z | |
| dc.date.available | 2026-07-07T08:39:55Z | |
| dc.description | Let $f$ be an analytic function on the unit disc which is in the Dirichlet class, so the Euclidean area of the image, counting multiplicity, is finite. The Euclidean length of a radial arc of hyperbolic length $ρ$ is then $o(ρ^1/2)$. In this note we consider the corresponding results when $f$ maps into the unit disc with the hyperbolic metric or the Riemann sphere with the spherical metric. Similar but not identical results hold. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0711.0170 | |
| dc.identifier | http://arxiv.org/abs/0711.0170 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141242 | |
| dc.subject | Complex Variables | |
| dc.subject | 30F45 (Primary); 30C45, 30C25 (Secondary) | |
| dc.title | Spherical and hyperbolic lengths of images of arcs | |
| dc.type | text |