Fractal percolation and quasisymmetric mappings

TL;DR

This paper investigates the conformal dimension of fractal percolation, demonstrating that it is almost surely strictly less than the Hausdorff dimension, highlighting a key geometric property of these fractals.

Contribution

It establishes that the conformal dimension of fractal percolation is almost surely smaller than its Hausdorff dimension, providing new insights into their geometric structure.

Findings

Conformal dimension is strictly less than Hausdorff dimension in fractal percolation.

Almost sure properties of fractal percolation are analyzed.

The study advances understanding of quasisymmetric mappings on fractals.

Abstract

We study the conformal dimension of fractal percolation and show that, almost surely, the conformal dimension of a fractal percolation is strictly smaller than its Hausdorff dimension.