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 2025Show all

5 papers · 1 filter

math.CO2025

Asymmetric sum-product theorems for Katz-Tao sets

Tuomas Orponen

I prove two variants of the $A B C$ sum-product theorem for $δ$ -separated sets $A, B, C \subset [0, 1]$ satisfying Katz-Tao spacing conditions. The main novelty is that the cardinality…

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 $μ$ on $[0, 1]^{2}$ such that $π_{θ} μ \in / L^{p}$ for every $θ \in S^{1}$ . 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 $L^{p}$ -norms of Fourier t…

math.CA2025

On the logarithmic equilibrium measure on curves

Damian Dąbrowski, Tuomas Orponen

Let $μ$ be the logarithmic equilibrium measure on a compact set $γ \subset R^{d}$ . We prove that $μ$ is absolutely continuous with respect to the length measure on the part…

Asymmetric sum-product theorems for Katz-Tao sets

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

A note on higher integrability of projections

Furstenberg set theorem for transversal families of functions

On the logarithmic equilibrium measure on curves

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