Illinois Journal of Mathematics

Lowering the Assouad dimension by quasisymmetric mappings

Jeremy T. Tyson

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Abstract

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

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

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138361

Digital Object Identifier
doi:10.1215/ijm/1258138361

Mathematical Reviews number (MathSciNet)
MR1878624

Zentralblatt MATH identifier
0989.30017

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

Citation

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


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