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

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Showing 2026 · math.CAShow all

3 papers · 2 filters

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

Furstenberg-type estimates under mild non-concentration assumptions

Tuomas Orponen, Pablo Shmerkin

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

math.CA2026

Nikodým maximal function with restricted directions

Tuomas Orponen, Hrit Roy

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