Jonathan M. Fraser

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math.CA2025

Hausdorff dimension of restricted Kakeya sets

Jonathan M. Fraser, Lijian Yang

A Kakeya set in $R^{n}$ is a compact set that contains a unit line segment $I_{e}$ in each direction $e \in S^{n - 1}$ . The Kakeya conjecture states that any Kakeya set in $\mat…

math.CA2024

On variants of the Furstenberg set problem

Jonathan M. Fraser

Given an integer $d \geq 2$ , $s \in (0, 1]$ , and $t \in [0, 2 (d - 1)]$ , suppose a set $X$ in $R^{d}$ has the following property: there is a collection of lines of packing dimens…