Bounded distortion homeomorphisms on ultrametric spaces
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-H\"older conditions for this class of ultrametric spaces.
Cite
@article{arxiv.1002.1652,
title = {Bounded distortion homeomorphisms on ultrametric spaces},
author = {Bruce Hughes and Álvaro Martínez-Pérez and Manuel A. Morón},
journal= {arXiv preprint arXiv:1002.1652},
year = {2012}
}
Comments
20 pages, 1 figure. To appear in Ann. Acad. Sci. Fenn. Math