Deformations on symbolic Cantor sets and ultrametric spaces
Complex Variables
2019-11-05 v1 Metric Geometry
Abstract
By introducing new deformations on symbolic Cantor sets and ultrametric spaces, we prove that doubling ultrametric spaces admit bilipschitz embedding into Cantor sets. If in addition the spaces are uniformly perfect, we show that they are quasisymmetrically equivalent to Cantor sets. As an application, we provide a new proof for a recent work of Heer (Anal. Geom. Metr. Spaces, 2017) regarding quasim\"obius uniformization of Cantor set.
Keywords
Cite
@article{arxiv.1911.01017,
title = {Deformations on symbolic Cantor sets and ultrametric spaces},
author = {Qingshan Zhou and Xining Li and Yaxiang Li},
journal= {arXiv preprint arXiv:1911.01017},
year = {2019}
}
Comments
8 pages, BMMS revised