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...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2010 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/42143 |
| Online Access: | https://hdl.handle.net/20.500.14352/42143 |
| Access Level: | Open access |
| Keyword: | 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 |
| Summary: | 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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