On the quasisymmetric minimality of homogeneous perfect sets

zbMATH Open1449.28009arXiv1801.09188MaRDI QIDQ5209097

Zhanqi Zhang, Yingqing Xiao

Publication date: 22 January 2020

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.

Full work available at URL: https://arxiv.org/abs/1801.09188

zbMATH Keywords

quasisymmetric mappinghomogeneous perfect setquasisymmetrically minimal set

Mathematics Subject Classification ID

Hausdorff and packing measures (28A78)

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