Locally minimal sets for conformal dimension

Christopher J. Bishop, Jeremy T. Tyson

Research output: Contribution to journalArticlepeer-review


We show that for each 1 ≤ α < d and K < ∞ there is a subset X of Rd such that dim(f(X)) ≥ α = dim(X) for every K-quasiconformal map, but such that dim(g(X)) can be made as small as we wish for some quasiconformal g, i.e., the conformal dimension of X is zero. These sets are then used to construct new examples of minimal sets for conformal dimension and sets where the conformal dimension is not attained.

Original languageEnglish (US)
Pages (from-to)361-373
Number of pages13
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Issue number2
StatePublished - 2001
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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