Damian Dąbrowski

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20232025

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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…

math.CA2024

On the dimension of $s$ -Nikodým sets

Damian Dąbrowski, Max Goering, Tuomas Orponen

Let $s \in [0, 1]$ . We show that a Borel set $N \subset R^{2}$ whose every point is linearly accessible by an $s$ -dimensional family of lines has Hausdorff dimension at mos…

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,…

On the logarithmic equilibrium measure on curves

On the dimension of s-Nikodým sets

How much can heavy lines cover?

On the dimension of $s$ -Nikodým sets