The structure of the semigroup of proper holomorphic mappings of a planar domain to the unit disc
| dc.creator | Bell, Steven R. | |
| dc.creator | Kaleem, Faisal | |
| dc.date | 2007-03-07 | |
| dc.date.accessioned | 2026-07-07T07:50:40Z | |
| dc.date.available | 2026-07-07T07:50:40Z | |
| dc.description | Given a bounded n-connected domain in the plane bounded by non-intersecting Jordan curves, and given one point on each boundary curve, L. Bieberbach proved that there exists a proper holomorphic mapping of the domain onto the unit disc that is an n-to-one branched covering with the properties that it extends continuously to the boundary and maps each boundary curve one-to-one onto the unit circle, and it maps each given point on the boundary to the point 1 in the unit circle. We modify a proof by H. Grunsky of Bieberbach's result to show that there is a rational function of 2n+2 complex variables that generates all of these maps. We also show how to generate all the proper holomorphic mappings to the unit disc via the rational function. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703200 | |
| dc.identifier | http://arxiv.org/abs/math/0703200 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125239 | |
| dc.subject | Complex Variables | |
| dc.subject | 30C40 | |
| dc.title | The structure of the semigroup of proper holomorphic mappings of a planar domain to the unit disc | |
| dc.type | text |