Topological Loewner theory on Riemann surfaces
We prove that topological evolution families on a Riemann surface S are rather trivial unless S is conformally equivalent to the unit disc or the punctuated unit disc. We also prove that, except for the torus where there is no non-trivial continuous Loewner chain, there is a topological evolution fa...
| Autores: | , |
|---|---|
| Tipo de documento: | artigo |
| Estado: | Versión aceptada para publicación |
| Data de publicação: | 2021 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/180968 |
| Acesso em linha: | https://hdl.handle.net/11441/180968 https://doi.org/10.1016/j.jmaa.2020.124525 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Evolution familiesLoewner chainsRiemann surfaces Loewner chainsRiemann surfaces Riemann surfaces |
| Resumo: | We prove that topological evolution families on a Riemann surface S are rather trivial unless S is conformally equivalent to the unit disc or the punctuated unit disc. We also prove that, except for the torus where there is no non-trivial continuous Loewner chain, there is a topological evolution family associated to any topological Loewner chain and, conversely, any topological evolution family comes from a topological Loewner chain on the same Riemann surface. |
|---|