Abstract 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 …

We study projections onto non-degenerate one-dimensional families of lines and planes in.
Using the classical potential theoretic approach of R. Kaufman, one can show that the …

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In this paper we use the theory of computing to study fractal dimensions of projections in
Euclidean spaces. A fundamental result in fractal geometry is Marstrand's projection …

Let 0≤ s≤ 1. A set K⊂ R2 is a Furstenberg s-set if for every unit vector e∈ S1, some line Le
parallel to e satisfies dimH [K∩ Le]≥ s. The Furstenberg set problem, introduced by T. Wolff …

We consider the Assouad dimensions of orthogonal projections of planar sets onto lines.
Our investigation covers both general and self‐similar sets. For general sets, the main result …

Let $ F\subset\mathbb {R}^{2} $, and let $\dim_ {\mathrm {A}} $ stand for Assouad
dimension. I prove that $\dim_ {\mathrm {A}}\pi_ {e}(F)\geq\min\{\dim_ {\mathrm {A}} F, 1\} …

This is a survey on recent developments on the Hausdorff dimension of projections and
intersections for general subsets of Euclidean spaces, with an emphasis on estimates of the …

We calculate the almost sure Hausdorff dimension of the random covering set lim
supn→∞(gn+ ξn) in d-dimensional torus Td, where the sets gn⊂ Td are parallelepipeds, or …

This paper contains the following $\delta $-discretised projection theorem for Ahlfors regular
sets in the plane. For all $ C,\epsilon> 0$ and $ s\in [0, 1] $, there exists $\kappa> 0$ such …