Bounded distortion homeomorphisms on ultrametric spaces

It is well-known that quasi-isometrics between R-trees induce power quasi-symmetric homeomorphisms between their ultrametric end spaces. This paper investigates power quasi-symmetric homeomorphisms between bounded, complete, uniformly perfect, ultrametric spaces (i.e., those ultrametric spaces arisi...

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Detalhes bibliográficos
Autores: Hughes, Bruce, Martínez Pérez, Álvaro, Alonso Morón, Manuel
Tipo de documento: artigo
Data de publicação:2010
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositório:Docta Complutense
Idioma:inglês
OAI Identifier:oai:docta.ucm.es:20.500.14352/42143
Acesso em linha:https://hdl.handle.net/20.500.14352/42143
Access Level:Acceso aberto
Palavra-chave:515.124
519.172
Tree
Real tree
Bushy tree
Ultrametric
End space
Quasi-isometry
Quasiconformal
Quasi-symmetric
PQ-symmetric
Doubling metric space
Topología
1210 Topología
Descrição
Resumo:It is well-known that quasi-isometrics between R-trees induce power quasi-symmetric homeomorphisms between their ultrametric end spaces. This paper investigates power quasi-symmetric homeomorphisms between bounded, complete, uniformly perfect, ultrametric spaces (i.e., those ultrametric spaces arising up to similarity as the end spaces of bushy trees). A bounded distortion property is found that characterizes power quasi-symmetric homeomorphisms between such ultrametric spaces that are also pseudo-doubling. Moreover, examples are given showing the extent to which the power quasi-symmetry of homeomorphisms is not captured by the quasiconformal and bi-Holder conditions for this class of ultrametric spaces.