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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.

Keywords

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

R2 v1 2026-06-21T16:11:45.135Z