46 citations · 268 across the 58 of their papers we have counts for
7 papers · 1 filter
Sixty Years of Fractal Projections
Kenneth Falconer, Jonathan Fraser, Xiong Jin
Sixty 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 lin…
On the equality of Hausdorff measure and Hausdorff content
Ábel Farkas, Jonathan M. Fraser
We are interested in situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result shows that this equality holds for a…
The Assouad dimension of randomly generated fractals
Jonathan M. Fraser, Jun Jie Miao, Sascha Troscheit
We consider several different models for generating random fractals including random self-similar sets, random self-affine carpets, and fractal percolation. In each setting we comp…
Some results in support of the Kakeya Conjecture
Jonathan M. Fraser, Eric J. Olson, James C. Robinson
A Besicovitch set is a subset of that contains a unit line segment in every direction and the famous Kakeya conjecture states that Besicovitch sets should have full dimensio…
On the dimensions of a family of overlapping self-affine carpets
Jonathan Fraser, Pablo Shmerkin
We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translati…
On the Assouad dimension of self-similar sets with overlaps
Jonathan. M. Fraser, Alexander. M. Henderson, Eric J. Olson +1
It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our mai…