Quasisymmetrically minimal homogeneous perfect sets
Complex Variables
2014-01-14 v3
Abstract
In \cite{ZW}, the notion of homogenous perfect set as a generalization of Cantor type sets is introduced. Their Hausdorff, lower box-counting, upper box-counting and packing dimensions are studied in \cite{ZW} and \cite{WW}. In this paper, we show that the homogenous perfect set be minimal for 1-dimensional quasisymmetric maps, which generalize the conclusion in \cite{MS} about the uniform Cantor cantor set to the homogenous perfect set.
Cite
@article{arxiv.1009.1799,
title = {Quasisymmetrically minimal homogeneous perfect sets},
author = {Yingqing Xiao},
journal= {arXiv preprint arXiv:1009.1799},
year = {2014}
}
Comments
13 pages