Topological Conformal Dimension
Metric Geometry
2023-06-23 v4
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.
Cite
@article{arxiv.1406.6623,
title = {Topological Conformal Dimension},
author = {Claudio A. DiMarco},
journal= {arXiv preprint arXiv:1406.6623},
year = {2023}
}
Comments
16 pages, revised after referee's reports. To appear in Conformal Geometry and Dynamics