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...
| Autores: | , , |
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| 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 |
| 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. |
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