A capacity approach to box and packing dimensions of projections of sets and exceptional directions

DOI10.4171/JFG/96zbMath1473.28007arXiv1901.11014OpenAlexW3111299647MaRDI QIDQ2031471

Kenneth J. Falconer

Publication date: 9 June 2021

Published in: Journal of Fractal Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.11014

zbMATH Keywords

capacityprojectionHausdorff dimensionbox dimensionpacking dimension

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Fractals (28A80)

Related Items

Assouad dimension influences the box and packing dimensions of orthogonal projections ⋮ Projection theorems for Hewitt-Stromberg and modified intermediate dimensions ⋮ The fractal structure of elliptical polynomial spirals ⋮ Dimensions of projected sets and measures on typical self-affine sets ⋮ Projection estimates for the lower Hewitt-Stromberg dimension ⋮ Box-counting dimension in one-dimensional random geometry of multiplicative cascades ⋮ Projection theorems for intermediate dimensions ⋮ Dimensions of fractional Brownian images ⋮ Intermediate Dimensions: A Survey

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hausdorff and packing dimensions of the images of random fields
• The discretized sum-product and projection theorems
• Orthogonal projections of discretized sets
• Packing dimension of the image of fractional Brownian motion
• Hausdorff dimension, projections, and the Fourier transform
• Box and packing dimensions of projections and dimension profiles
• Sixty Years of Fractal Projections
• Restricted Radon Transforms and Projections of Planar Sets
• Packing Measure, and its Evaluation for a Brownian Path
• Hausdorff dimension and the exceptional set of projections
• Two definitions of fractional dimension
• Hausdorff dimension, orthogonal projections and intersections with planes
• Hausdorff dimension and exceptional sets of linear transformations
• Packing dimensions of projections and dimension profiles
• The packing dimension of projections and sections of measures
• Projection theorems for box and packing dimensions
• A Capacity Approach to Box and Packing Dimensions of Projections and Other Images
• Fourier Analysis and Hausdorff Dimension
• On Hausdorff dimension of projections
• Some Fundamental Geometrical Properties of Plane Sets of Fractional Dimensions