On spherical invariance
In 1964 Pommerenke introduced the notion of linear invariant family for locally injective analytic functions defined in the unit disk of the complex plane. Following Ma and Minda (who extended this notion to spherical geometry), we consider in this paper locally injective meromorphic functions in th...
- Autores:
-
Arbeláez, Hugo
Mejía, Diego
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2011
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/39451
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/39451
http://bdigital.unal.edu.co/29548/
- Palabra clave:
- Spherical invariance
Spherical order
Schwarzian derivative
Normal function
Uniformly perfect
30D30
30D45
30C45
30F45
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | In 1964 Pommerenke introduced the notion of linear invariant family for locally injective analytic functions defined in the unit disk of the complex plane. Following Ma and Minda (who extended this notion to spherical geometry), we consider in this paper locally injective meromorphic functions in the unit disk. More precisely, we study families of such functions for which a certain invariant, called spherical order, is finite. Several consequences on the finiteness of the spherical order are explored, in particular the connection with the Schwarzian and normal orders, and with uniform perfectness. |
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