Tuomas Orponen

activity

20102026

most citedOn restricted families of projections in R^3

52 citations · 367 across the 81 of their papers we have counts for

collaborators

Showing 2021 · math.CAShow all

4 papers · 2 filters

math.CA2021

On a continuous Sárközy type problem

Borys Kuca, Tuomas Orponen, Tuomas Sahlsten

We prove that there exists a constant $ε > 0$ with the following property: if $K \subset R^{2}$ is a compact set which contains no pair of the form $\{x, x + (z,…

math.CA2021

Integrability of orthogonal projections, and applications to Furstenberg sets

Damian Dąbrowski, Tuomas Orponen, Michele Villa

Let $G (d, n)$ be the Grassmannian manifold of $n$ -dimensional subspaces of $R^{d}$ , and let $π_{V} : R^{d} \to V$ be the orthogonal projection. We p…

math.CA2021★ 1 cited

On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane

Tuomas Orponen, Pablo Shmerkin

Let $0 \leq s \leq 1$ and $0 \leq t \leq 2$ . An $(s, t)$ -Furstenberg set is a set $K \subset R^{2}$ with the following property: there exists a line set $L$ of Ha…

math.CA2021

On arithmetic sums of Ahlfors-regular sets

Tuomas Orponen

Let $A, B \subset R$ be closed Ahlfors-regular sets with dimensions $dim_{H} A =: α$ and $dim_{H} B =: β$ . I prove that $$\dim_{\mathrm{H}} [A + θB] \ge…