Illinois Journal of Mathematics

Lowering the Assouad dimension by quasisymmetric mappings

Jeremy T. Tyson

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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.

Article information

Illinois J. Math., Volume 45, Number 2 (2001), 641-656.

First available in Project Euclid: 13 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30C65: Quasiconformal mappings in $R^n$ , other generalizations
Secondary: 28A78: Hausdorff and packing measures 54F45: Dimension theory [See also 55M10]


Tyson, Jeremy T. Lowering the Assouad dimension by quasisymmetric mappings. Illinois J. Math. 45 (2001), no. 2, 641--656. doi:10.1215/ijm/1258138361.

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