Fractal Curves and Rugs of Prescribed Conformal Dimension

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.

arXiv comment14 pages, 1 figure, Topology and Its Applications (2018)

References in corpus (2)

• Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary
• Topological Conformal Dimension

Cited by in corpus (2)

• Lipschitz clustering in metric spaces
• Bounded geometry and $p$-harmonic functions under uniformization and hyperbolization