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...

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Detalhes bibliográficos
Autores: Contreras Márquez, Manuel Domingo, Díaz Madrigal, Santiago
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
Descrição
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.