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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80 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 -dimensional in all directions. This disproves the visibility conjecture. The value c…

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.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…

math.CA2025

A note on higher integrability of projections

Tuomas Orponen

Let and . I construct a -Frostman Borel measure on such that for every . This answers a question of P…

math.CA2025

Furstenberg set theorem for transversal families of functions

Tuomas Orponen, Aleksi Pyörälä, Guangzeng Yi

We prove an extension of the Furstenberg set theorem to families of graphs satisfying a transversality condition. We apply the result to derive bounds on -norms of Fourier t…