Add to ORKGWe use recent advances on the discretized sum-product problem to obtain new bounds on the Hausdorff dimension of planar $(\alpha,2\alpha)$-Fursterberg sets. This provides a quantitative improvement to the $2\alpha+\epsilon$ bound of H\'era-Shmerkin-Yavicoli. In particular, we show that every $1/2$-Furstenberg set has dimension at least $1 + 1/4536$.Comment: 28 pages, 1 figure. v2: revised based on referee comments; results are unchange
We obtain new lower bounds on the Hausdorff dimension of distance sets and pinned distance sets of p...
We prove that every Besicovitch set in ℝ^3 must have Hausdorff dimension at least 5/2 + ϵ_0 for some...
We prove that any Besicovitch set in $\mathbb{R}^3$ must have Hausdorff dimension at least $5/2+\eps...
In this survey we collect and discuss some recent results on the so called “Furstenberg set problem”...
We show that the Hausdorff dimension of $(s,t)$-Furstenberg sets is at least $s+t/2+\epsilon$, where...
AbstractIn this paper we study the problem of estimating the generalized Hausdorff dimension of Furs...
In this paper we study the behavior of the size of Furstenberg sets with respect to the size of the ...
Let $0 \leq s \leq 1$ and $0 \leq t \leq 2$. An $(s,t)$-Furstenberg set is a set $K \subset \mathbb{...
We make progress on several interrelated problems at the intersection of geometric measure theory, a...
For α in (0, 1], a subset E of R2 is called Furstenberg set of type α or Fα-set if for each directio...
In this paper we study the problem of estimating the generalized Hausdorff dimension of Furstenberg ...
In this paper, we show that circular $(s,t)$-Furstenberg sets in $\mathbb R^2$ have Hausdorff dimens...
JMF is financially supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Resear...
En esta tesis se estudian dos problemas del Análisis Armónico clásico desde el punto de vista de la...
In this paper we study the problem of estimating the generalized Hausdorff dimension of Furstenberg ...
We obtain new lower bounds on the Hausdorff dimension of distance sets and pinned distance sets of p...
We prove that every Besicovitch set in ℝ^3 must have Hausdorff dimension at least 5/2 + ϵ_0 for some...
We prove that any Besicovitch set in $\mathbb{R}^3$ must have Hausdorff dimension at least $5/2+\eps...
In this survey we collect and discuss some recent results on the so called “Furstenberg set problem”...
We show that the Hausdorff dimension of $(s,t)$-Furstenberg sets is at least $s+t/2+\epsilon$, where...
AbstractIn this paper we study the problem of estimating the generalized Hausdorff dimension of Furs...
In this paper we study the behavior of the size of Furstenberg sets with respect to the size of the ...
Let $0 \leq s \leq 1$ and $0 \leq t \leq 2$. An $(s,t)$-Furstenberg set is a set $K \subset \mathbb{...
We make progress on several interrelated problems at the intersection of geometric measure theory, a...
For α in (0, 1], a subset E of R2 is called Furstenberg set of type α or Fα-set if for each directio...
In this paper we study the problem of estimating the generalized Hausdorff dimension of Furstenberg ...
In this paper, we show that circular $(s,t)$-Furstenberg sets in $\mathbb R^2$ have Hausdorff dimens...
JMF is financially supported by an EPSRC Standard Grant (EP/R015104/1) and a Leverhulme Trust Resear...
En esta tesis se estudian dos problemas del Análisis Armónico clásico desde el punto de vista de la...
In this paper we study the problem of estimating the generalized Hausdorff dimension of Furstenberg ...
We obtain new lower bounds on the Hausdorff dimension of distance sets and pinned distance sets of p...
We prove that every Besicovitch set in ℝ^3 must have Hausdorff dimension at least 5/2 + ϵ_0 for some...
We prove that any Besicovitch set in $\mathbb{R}^3$ must have Hausdorff dimension at least $5/2+\eps...