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Bounded distortion homeomorphisms on ultrametric spaces

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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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
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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