3 papers
math.MG2026
Seventy Years of Fractal Projections
Kenneth J. Falconer
Seventy years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto l…
math.MG2026
Frostman and Fourier characterisations of fractal dimensions
Kenneth J. Falconer, Shuqin Zhang
We examine Frostman-type characterisations and other extremal measure criteria for a range of fractal dimensions of sets. In particular we derive properties of the less familiar mo…
math.MG2024
Fractal percolation on statistically self-affine carpets
Kenneth Falconer, Tianyi Feng
We consider a random self-affine carpet based on an subdivision of rectangles and a probability . Starting by dividing into an grid of…