Uniformization of Cantor sets with bounded geometry
Metric Geometry
2022-02-23 v5
Abstract
In this note we provide a quasisymmetric taming of uniformly perfect and uniformly disconnected sets that generalizes a result of MacManus from 2 to higher dimensions. In particular, we show that a compact subset of is uniformly perfect and uniformly disconnected if and only if it is ambiently quasiconformal to the standard Cantor set in .
Keywords
Cite
@article{arxiv.1609.08763,
title = {Uniformization of Cantor sets with bounded geometry},
author = {Vyron Vellis},
journal= {arXiv preprint arXiv:1609.08763},
year = {2022}
}
Comments
13 pages. This is a small part of an older manuscript called "Extension properties of planar uniform domains"