# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1905.11080