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<p>We study properties of weakly quasisymmetric mappings in metric measure spaces. Firstly, we establish weak quasisymmetric analogue of a result of Heinonen, proving that a metric space is weakly quasisymmetrically homeomorphic to an Ahlfors regular space if and only if it is perfect and homogeneous. Next, we generalize results of David and Semmes and show that every bounded, complete, doubling, perfect, and uniformly disconnected metric space is weakly quasisymmetrically homeomorphic to a Cantor set.</p>

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Weakly Quasisymmetric Mappings and Cantor Sets

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • Qingshan Zhou,
  • Zhoucheng Zheng,
  • Si Chen,
  • Antti Rasila

摘要

We study properties of weakly quasisymmetric mappings in metric measure spaces. Firstly, we establish weak quasisymmetric analogue of a result of Heinonen, proving that a metric space is weakly quasisymmetrically homeomorphic to an Ahlfors regular space if and only if it is perfect and homogeneous. Next, we generalize results of David and Semmes and show that every bounded, complete, doubling, perfect, and uniformly disconnected metric space is weakly quasisymmetrically homeomorphic to a Cantor set.