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

92 papers

math.CA2026

Planar sets with large visible parts

Tuomas Orponen

I construct a compact subset of the plane whose visible parts are -dimensional in all directions. This disproves the visibility conjecture. The value c…

math.CO2026

Visibility problem in the plane

Tuomas Orponen, Alex Rutar

We disprove the visibility conjecture in the plane and prove the sharp upper bound for the almost-sure dimension of visible parts. Precisely, let be a co…

math.CA2026

Furstenberg-type estimates under mild non-concentration assumptions

Tuomas Orponen, Pablo Shmerkin

We prove sharp -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 associated to a direction set . We show that the quasi-Assouad dimension $s := \dim_{\math…

math.CO2025

Asymmetric sum-product theorems for Katz-Tao sets

Tuomas Orponen

I prove two variants of the sum-product theorem for -separated sets satisfying Katz-Tao spacing conditions. The main novelty is that the cardinality…

math.CA2025

Uniformly perfect measures on strictly convex planar graphs are -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…