Deformations on symbolic Cantor sets and ultrametric spaces
arXiv:1911.01017
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 quasimöbius uniformization of Cantor set.
8 pages, BMMS revised