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 2015 · math.CAShow all

5 papers · 2 filters

math.CA2015

Quasisymmetric maps on Kakeya sets

Tuomas Orponen

I show that $L^{p} - L^{q}$ estimates for the Kakeya maximal function yield lower bounds for the conformal dimension of Kakeya sets, and upper bounds for how much quasisymmetries can…

math.CA2015★ 37 cited

On the distance sets of AD-regular sets

Tuomas Orponen

I prove that if $\emptyset \neq = K \subset R^{2}$ is a compact $s$ -Ahlfors-David regular set with $s \geq 1$ , then $dim_{p} D (K) = 1,$ where $D(K) := \{|x - y|…

math.CA2015★ 16 cited

Hausdorff dimension, intersection of projections and exceptional plane sections

Pertti Mattila, Tuomas Orponen

This paper contains new results on two classical topics in fractal geometry: projections, and intersections with affine planes. To keep the notation of the abstract simple, we rest…

math.CA2015★ 14 cited

The Assouad dimensions of projections of planar sets

Jonathan M. Fraser, Tuomas Orponen

We consider the Assouad dimensions of orthogonal projections of planar sets onto lines. Our investigation covers both general and self-similar sets. For general sets, the main resu…

math.CA2015★ 7 cited

Projections of planar sets in well-separated directions

Tuomas Orponen

First, let $K \subset B (0, 1) \subset R^{2}$ be a set with $H_{\infty}^{1} (K) \sim 1$ , and write $π_{e} (K)$ for the orthogonal projection of $K$ into the line spa…