Tuomas Orponen

activity

20142024

most citedImproving Kaufman's exceptional set estimate for packing dimension

4 citations · 7 across the 4 of their papers we have counts for

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math.CA2023

How much can heavy lines cover?

Damian Dąbrowski, Tuomas Orponen, Hong Wang

One formulation of Marstrand's slicing theorem is the following. Assume that $t \in (1, 2]$ , and $B \subset R^{2}$ is a Borel set with $H^{t} (B) < \infty$ . Then,…

math.CA2016★ 4 cited

Improving Kaufman's exceptional set estimate for packing dimension

Tuomas Orponen

Given $0 < s < 1$ , I prove that there exists a constant $ε = ε (s) > 0$ such that the following holds. Let $K \subset R^{2}$ be a Borel set with $H^{1} (K) > 0$ , an…

math.CA2014★ 3 cited

A discretised projection theorem in the plane

Tuomas Orponen

The main result of this paper is that for any $1/2 \leq s < 2 - 2 \approx 0.5858$ , there is a number $σ = σ (s) < s$ with the following property. Let $δ > 0$ be small, assume t…