On the quasisymmetric minimality of homogeneous perfect sets

Abstract

Z. Wen and J. Wu introduced the notion of homogeneous perfect sets as a generalization of Cantor type sets and determined their exact Hausdorff dimension based on the length of their fundamental intervals and the gaps between them. In this paper, we considered the minimality of the homogeneous perfect sets with Hausdorff dimension 1 and proved they are 1-dimensional quasisymmetrically minimal under some conditions.