Quasisymmetrically minimal homogeneous perfect sets
Abstract
In 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 ZW and WW. In this paper, we show that the homogenous perfect set be minimal for 1-dimensional quasisymmetric maps, which generalize the conclusion in MS about the uniform Cantor cantor set to the homogenous perfect set.
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