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Summer 2001 Lowering the Assouad dimension by quasisymmetric mappings
Jeremy T. Tyson
Illinois J. Math. 45(2): 641-656 (Summer 2001). DOI: 10.1215/ijm/1258138361

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.

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Jeremy T. Tyson. "Lowering the Assouad dimension by quasisymmetric mappings." Illinois J. Math. 45 (2) 641 - 656, Summer 2001. https://doi.org/10.1215/ijm/1258138361

Information

Published: Summer 2001
First available in Project Euclid: 13 November 2009

zbMATH: 0989.30017
MathSciNet: MR1878624
Digital Object Identifier: 10.1215/ijm/1258138361

Subjects:
Primary: 30C65
Secondary: 28A78, 54F45

Rights: Copyright © 2001 University of Illinois at Urbana-Champaign

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Vol.45 • No. 2 • Summer 2001
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