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arXiv · 1002.1652

Bounded distortion homeomorphisms on ultrametric spaces

Bruce Hughes·Álvaro Martínez-Pérez·Manuel A. Morón
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Abstract

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-Hölder conditions for this class of ultrametric spaces.

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Bruce Hughes, Álvaro Martínez-Pérez, Manuel A. Morón. 2010-02-09. Bounded distortion homeomorphisms on ultrametric spaces. https://arxiv.org/abs/1002.1652

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