Quasisymmetrically minimal homogeneous perfect sets

Details Quasisymmetrically minimal homogeneous perfect sets Quasisymmetrically minimal homogeneous perfect sets

2010-09-09

arxiv.org/abs/1009.1799v3

Mathematics

Complex Variables

13 pages

Scientific paper

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.

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