Tuomas Orponen

activity

20242026

most citedProjections, Furstenberg sets, and the

A B C

sum-product problem

2 citations · 2 across the 4 of their papers we have counts for

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13 papers · 1 filter

math.CA2026

Planar sets with large visible parts

Tuomas Orponen

I construct a compact subset of the plane whose visible parts are $\frac{3}{2}$ -dimensional in all directions. This disproves the visibility conjecture. The value $\frac{3}{2}$ c…

math.CA2026★ 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…

math.CA2026

Furstenberg-type estimates under mild non-concentration assumptions

Tuomas Orponen, Pablo Shmerkin

We prove sharp $I^´$ -discretised versions of some variants of the Furstenberg set problem under weaker or different non-concentration assumptions compared to previous works.

math.CA2026

NikodÃ½m maximal function with restricted directions

Tuomas Orponen, Hrit Roy

We study the planar NikodÃ½m maximal operator $N_{I^; I^´}$ associated to a direction set $I^ \subset S^{1}$ . We show that the quasi-Assouad dimension $s := \dim_{\…

math.CA2025

Uniformly perfect measures on strictly convex planar graphs are $L^{2}$ -flattening

Amir Algom, Tuomas Orponen

Uniformly perfect measures are a common generalisation of Ahlfors regular measures, self-conformal measures on the line, and their push-forwards under sufficiently regular maps. We…

math.CA2025

A note on higher integrability of projections

Tuomas Orponen

Let $t \in [1, 2)$ and $p > 2/ (2 - t)$ . I construct a $t$ -Frostman Borel measure $I^¼$ on $[0, 1]^{2}$ such that $I ¨ _{I^} ¸ I^¼ \in / L^{p}$ for every $I^¸ \in S^{1}$ . This answers a question…

Planar sets with large visible parts

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

Furstenberg-type estimates under mild non-concentration assumptions

NikodÃ½m maximal function with restricted directions

Uniformly perfect measures on strictly convex planar graphs are L2-flattening

A note on higher integrability of projections

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

Uniformly perfect measures on strictly convex planar graphs are $L^{2}$ -flattening