This analysis reveals quasisymmetric minimality in homogeneous perfect sets, indicating a new frontier in fractal geometry.
The quasisymmetric minimality for fractal sets is a hot research topic for scholars focused on the fractal geometry and quasisymmetric mappings. In this paper, we study the quasisymmetric minimality on packing dimension for homogeneous perfect sets. By using some mathematical tools such as the mass distribution principle, we find that a special class of homogeneous perfect sets with packing dimension 1 is quasisymmetrically packing minimal. Our result generalizes the results in the references.
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Liu et al. (2025) studied this question.
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