Hughes, Bruce and Martínez Pérez , Álvaro and Morón, Manuel A.
(2010)
*Bounded distortion homeomorphisms on ultrametric spaces.*
Annales academiae scientiarum fennicae-mathematica, 35
(2).
pp. 473-492.
ISSN 1239-629X

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Official URL: http://arxiv.org/pdf/1002.1652v2.pdf

## Abstract

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.

Item Type: | Article |
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Uncontrolled Keywords: | Tree; real tree; bushy tree; ultrametric; end space; quasi-isometry; quasiconformal; quasi-symmetric; PQ-symmetric; doubling metric space |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 15030 |

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Deposited On: | 26 Apr 2012 08:12 |

Last Modified: | 06 Feb 2014 10:14 |

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