Year: 2021
Type: article
Abstract: In this note we provide a quasisymmetric taming of uniformly perfect and uniformly disconnected sets that generalizes a result of MacManus [Rev. Mat. Iberoamericana 15 (1999), pp. 267–277] from 2 to higher dimensions. In particular, we show that a compact subset of Rn \mathbb {R}^n is uniformly perfect and uniformly disconnected if and only if it is ambiently quasiconformal to the standard Cantor set C \mathcal {C} in Rn+1 \mathbb {R}^{n+1} .
DOI: 10.1090/ecgd/360
Author: Vyron Vellis
Institution: University of Tennessee at Knoxville
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W3118725282