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 2022 · math.CAShow all

7 papers · 2 filters

math.CA2022★ 3 cited

A note on Kakeya sets of horizontal and $S L (2)$ lines

Katrin Fässler, Tuomas Orponen

We consider unions of $S L (2)$ lines in $R^{3}$ . These are lines of the form $L = (a, b, 0) + span (c, d, 1),$ where $a d - b c = 1$ . We show that if $L$ is a…

math.CA2022

Vertical projections in the Heisenberg group via cinematic functions and point-plate incidences

Katrin Fässler, Tuomas Orponen

Let ${π_{e} : H \to W_{e} : e \in S^{1}}$ be the family of vertical projections in the first Heisenberg group $H$ . We prove that if $K \subset \ma…

math.CA2022★ 2 cited

Kaufman and Falconer estimates for radial projections and a continuum version of Beck's Theorem

Tuomas Orponen, Pablo Shmerkin, Hong Wang

We provide several new answers on the question: how do radial projections distort the dimension of planar sets? Let $X, Y \subset R^{2}$ be non-empty Borel sets. If $X$ is…

math.CA2022★ 1 cited

On exceptional sets of radial projections

Tuomas Orponen, Pablo Shmerkin

We prove two new exceptional set estimates for radial projections in the plane. If $K \subset R^{2}$ is a Borel set with $dim_{H} K > 1$ , then $$\dim_{\mathrm{H}…

math.CA2022

Additive properties of fractal sets on the parabola

Tuomas Orponen

Let $0 \leq s \leq 1$ , and let $P := {(t, t^{2}) \in R^{2} : t \in [- 1, 1]}$ . If $K \subset P$ is a closed set with $dim_{H} K = s$ , it is not…

math.CA2022★ 5 cited

Structure of sets with nearly maximal Favard length

Alan Chang, Damian Dąbrowski, Tuomas Orponen +1

Let $E \subset B (1) \subset R^{2}$ be an $H^{1}$ measurable set with $H^{1} (E) < \infty$ , and let $L \subset R^{2}$ be a line segment with $\mat…