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Conformal Geometry and Dynamics

ISSN 1088-4173

 

 

Topological conformal dimension


Author: Claudio A. DiMarco
Journal: Conform. Geom. Dyn. 19 (2015), 19-34
MSC (2010): Primary 28A80, 30L10; Secondary 28A78, 54F45
DOI: https://doi.org/10.1090/S1088-4173-2015-00274-X
Published electronically: January 26, 2015
MathSciNet review: 3303179
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Abstract: We investigate a quasisymmetrically invariant counterpart of the topological Hausdorff dimension of a metric space. This invariant, called the topological conformal dimension, gives a lower bound on the topological Hausdorff dimension of quasisymmetric images of the space. We obtain results concerning the behavior of this quantity under products and unions, and compute it for some classical fractals. The range of possible values of the topological conformal dimension is also considered, and we show that this quantity can be fractional.


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Additional Information

Claudio A. DiMarco
Affiliation: 215 Carnegie, Mathematics Department, Syracuse University, Syracuse, New York 13244-1150
Email: cdimarco@syr.edu

DOI: https://doi.org/10.1090/S1088-4173-2015-00274-X
Keywords: Metric space, conformal dimension, topological dimension, quasisymmetric map, Cantor sets
Received by editor(s): June 19, 2014
Received by editor(s) in revised form: December 5, 2014, and December 29, 2014
Published electronically: January 26, 2015
Article copyright: © Copyright 2015 American Mathematical Society