arXiv 1002.16522010-02-09math.MGmath.GNmath.GT

Bounded distortion homeomorphisms on ultrametric spaces

Bruce Hughes, Álvaro Martínez-Pérez, Manuel A. Morón

备注：: 20 pages, 1 figure. To appear in Ann. Acad. Sci. Fenn. Math
发表信息：: Annales Academiae Scientiarum Fennicae. Mathematica 35 (2010), pages 473-492

英文摘要：

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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