Explanipedia

Bounds on the dimension of lineal extensions Open

Ryan E. G. Bushling, Jacob B. Fiedler · 2025

Let E \subseteq \mathbb{R}^{n} be a union of line segments and F \subseteq \mathbb{R}^{n} the set obtained from E by extending each line segment in E to a full line. Keleti’s line segment extension conjecture posits that the Hausdorff dime…

Universal Sets for Projections Open

Jacob B. Fiedler, D. M. Stull · 2024

We investigate variants of Marstrand's projection theorem that hold for sets of directions and classes of sets in $\mathbb{R}^2$. We say that a set of directions $D \subseteq\mathcal{S}^1$ is $\textit{universal}$ for a class of sets if, fo…

Pinned distances of planar sets with low dimension Open

Jacob B. Fiedler, D. M. Stull · 2024

In this paper, we give improved bounds on the Hausdorff dimension of pinned distance sets of planar sets with dimension strictly less than one. As the planar set becomes more regular (i.e., the Hausdorff and packing dimension become closer…

A study guide for "On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" after T. Orponen and P. Shmerkin Open

Jacob B. Fiedler, Guo-Dong Hong, Donggeun Ryou, Shukun Wu · 2024

This article is a study guide for ``On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" by Orponen and Shmerkin. We begin by introducing Furstenberg set problem and exceptional set of projections and pro…

Bounds on the dimension of lineal extensions Open

Ryan E. G. Bushling, Jacob B. Fiedler · 2024

Let $E \subseteq \mathbb{R}^n$ be a union of line segments and $F \subseteq \mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$ to a full line. Keleti's line segment extension conjecture posits that the Hausdorff …

Dimension of Pinned Distance Sets for Semi-Regular Sets Open

Jacob B. Fiedler, D. M. Stull · 2023

We prove that if $E\subseteq \R^2$ is analytic and $1

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