Conformal dimension of the antenna set

Christopher J. Bishop, Jeremy T. Tyson

Research output: Contribution to journalArticlepeer-review


We show that the self-similar set known as the "antenna set" has the property that infy d\m(f(X)) = 1 (where the infimum is over all quasiconformal mappings of the plane), but that this infimum is not attained by any quasiconformal map; indeed, is not attained for any quasisymmetric map into any metric space.

Original languageEnglish (US)
Pages (from-to)3631-3636
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number12
StatePublished - 2001
Externally publishedYes


  • Conformai dimension
  • Hausdorff dimension
  • Quasiconformal map
  • Selfsimilar sets

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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