Fractal percolation is unrectifiable

DOI10.1016/j.aim.2021.107906OpenAlexW3185716426MaRDI QIDQ822704

Tuomas Pöyhtäri, Esa Järvenpää, Maarit Järvenpää, Zoltán Buczolich, Tamás Keleti

Publication date: 23 September 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.11796

zbMATH Keywords

fractal percolationunrectifiability

Mathematics Subject Classification ID

Fractals (28A80) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Cites Work

• Unnamed Item
• Unnamed Item
• Projections of the natural measure for percolation fractals
• Dimension (In)equalities and Hölder continuous curves in fractal percolation
• Connectivity properties of Mandelbrot's percolation process
• On the geometry of random Cantor sets and fractal percolation
• Connectivity in fractal percolation
• Sur certaines martingales de Benoit Mandelbrot
• A lower bound on the box-counting dimension of crossings in fractal percolation
• Geometric measure theory.
• On the length of the shortest crossing in the super-critical phase of Mandelbrot's percolation process
• The dimension of projections of fractal percolations
• Hölder curves and parameterizations in the Analyst's traveling salesman theorem
• Geometry of measures in real dimensions via Hölder parameterizations
• Visible parts of fractal percolation
• Hausdorff measures, Hölder continuous maps and self-similar fractals
• Probability on Graphs
• k-Dimensional Regularity Classifications for s-Fractals
• Probability with Martingales
• Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier
• Percolation
• On the parametrization of self-similar and other fractal sets
• Projections of fractal percolations