Bounded distortion homeomorphisms on ultrametric spaces

Details Bounded distortion homeomorphisms on ultrametric spaces Bounded distortion homeomorphisms on ultrametric spaces

2010-02-08

arxiv.org/abs/1002.1652v2

Mathematics

Metric Geometry

20 pages, 1 figure. To appear in Ann. Acad. Sci. Fenn. Math

Scientific paper

It is well-known that quasi-isometries 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-H\"older conditions for this class of ultrametric spaces.

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