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 2023 · math.CAShow all

5 papers · 2 filters

math.CA2023

On the Hausdorff dimension of radial slices

Tuomas Orponen

Let $t \in (1, 2)$ , and let $B \subset R^{2}$ be a Borel set with $dim_{H} B > t$ . I show that $$\mathcal{H}^{1}(\{e \in S^{1} : \dim_{\mathrm{H}} (B \cap \ell_{x…

math.CA2023

How much can heavy lines cover?

Damian Dąbrowski, Tuomas Orponen, Hong Wang

One formulation of Marstrand's slicing theorem is the following. Assume that $t \in (1, 2]$ , and $B \subset R^{2}$ is a Borel set with $H^{t} (B) < \infty$ . Then,…

math.CA2023

On the Fourier decay of multiplicative convolutions

Tuomas Orponen, Nicolas de Saxcé, Pablo Shmerkin

We prove the following. Let $μ_{1}, \dots, μ_{n}$ be Borel probability measures on $[- 1, 1]$ such that $μ_{j}$ has finite $s_{j}$ -energy for certain indices $s_{j} \in (0, 1]$ with $s_{…

math.CA2023★ 1 cited

On the Hausdorff dimension of circular Furstenberg sets

Katrin Fässler, Jiayin Liu, Tuomas Orponen

For $0 \leq s \leq 1$ and $0 \leq t \leq 3$ , a set $F \subset R^{2}$ is called a circular $(s, t)$ -Furstenberg set if there exists a family of circles $S$ of Haus…

math.CA2023★ 2 cited

Projections, Furstenberg sets, and the $A B C$ sum-product problem

Tuomas Orponen, Pablo Shmerkin

We make progress on two interrelated problems at the intersection of geometric measure theory, additive combinatorics and harmonic analysis: the discretised sum-product problem, an…

On the Hausdorff dimension of radial slices

How much can heavy lines cover?

On the Fourier decay of multiplicative convolutions

On the Hausdorff dimension of circular Furstenberg sets

Projections, Furstenberg sets, and the ABC sum-product problem

Projections, Furstenberg sets, and the $A B C$ sum-product problem