Fractal Curves and Rugs of Prescribed Conformal Dimension
Metric Geometry
2018-08-14 v2
Abstract
We construct Jordan arcs of prescribed conformal dimension which are minimal for conformal dimension. These curves are used to design fractal rugs, similar to Rickman's rug, that are also minimal for conformal dimension. These fractal rugs could potentially settle a standing conjecture regarding the existence of metric spaces of prescribed topological conformal dimension.
Keywords
Cite
@article{arxiv.1509.09219,
title = {Fractal Curves and Rugs of Prescribed Conformal Dimension},
author = {Claudio A. DiMarco},
journal= {arXiv preprint arXiv:1509.09219},
year = {2018}
}
Comments
14 pages, 1 figure, Topology and Its Applications (2018)