Lowering the Assouad dimension by quasisymmetric mappings

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We study the relationship between the Assouad dimension and quasisymmetric mappings, showing that spaces of dimension strictly less than one can be quasisymmetrically deformed onto spaces of arbitrarily small dimension. We conjecture that this fact holds also for the Hausdorff dimension, and our results yield several corollaries which provide partial support for this conjecture. The proofs make use of connections between Assouad dimension, porosity, and ultrametrics.

Original languageEnglish (US)
Pages (from-to)641-656
Number of pages16
JournalIllinois Journal of Mathematics
Issue number2
StatePublished - 2001
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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