Sets of minimal hausdorff dimension for quasiconformal maps

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For any 1 ≤ a ≤ n, there is a compact set E ⊂ ℝn of (Hausdorff) dimension α whose dimension cannot be lowered by any quasiconformal map f : ℝn → ℝn. We conjecture that no such set exists in the case α < 1. More generally, we identify a broad class of metric spaces whose Hausdorff dimension is minimal among quasisymmetric images.

Original languageEnglish (US)
Pages (from-to)3361-3367
Number of pages7
JournalProceedings of the American Mathematical Society
Issue number11
StatePublished - 2000
Externally publishedYes


  • Generalized modulus
  • Hausdorff dimension
  • Quasiconformal maps

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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