Pablo Shmerkin

activity

20042025

most citedLocal entropy averages and projections of fractal measures

92 citations · 502 across the 56 of their papers we have counts for

collaborators

Showing 2022Show all

3 papers · 1 filter

math.CA2022★ 2 cited

Dimensions of Furstenberg sets and an extension of Bourgain's projection theorem

Pablo Shmerkin, Hong Wang

We show that the Hausdorff dimension of $(s, t)$ -Furstenberg sets is at least $s + t /2 + ε$ , where $ε > 0$ depends only on $s$ and $t$ . This improves the previously best known bound for $…

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}…