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 2020Show all

4 papers · 1 filter

math.CA2020

On the packing dimension of Furstenberg sets

Pablo Shmerkin

We prove that if $α \in (0, 1/2]$ , then the packing dimension of a set $E \subset R^{2}$ for which there exists a set of lines of dimension $1$ intersecting $E$ in dimension $\g…

math.CA2020

Covering the Sierpiński carpet with tubes

Aleksi Pyörälä, Pablo Shmerkin, Ville Suomala +1

We show that non-trivial $\times N$ -invariant sets in $[0, 1]^{d}$ , such as the Sierpiński carpet and the Sierpiński sponge, are tube-null, that is, they can be covered by a union of…

math.CA2020★ 2 cited

A nonlinear version of Bourgain's projection theorem

Pablo Shmerkin

We prove a version of Bourgain's projection theorem for parametrized families of $C^{2}$ maps, that refines the original statement even in the linear case. As one application, we sho…

math.CA2020

An improved bound for the dimension of $(α, 2 α)$ -Furstenberg sets

Kornélia Héra, Pablo Shmerkin, Alexia Yavicoli

We show that given $α \in (0, 1)$ there is a constant $c = c (α) > 0$ such that any planar $(α, 2 α)$ -Furstenberg set has Hausdorff dimension at least $2 α + c$ . This improves several pre…

On the packing dimension of Furstenberg sets

Covering the Sierpiński carpet with tubes

A nonlinear version of Bourgain's projection theorem

An improved bound for the dimension of (α,2α)-Furstenberg sets

An improved bound for the dimension of $(α, 2 α)$ -Furstenberg sets