Author

Bo-Cheng Liu

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Preprint Sep 2026

Some constructions of restricted Kakeya sets

In this paper, we consider Kakeya sets with the additional restriction that centers of the unit line segments belong to a given set. In particular, for every uncountable Borel set $A\subset\mathbb{R}^d$, $d\geq 2$, we construct a compact subset of $\mathbb{R}^d$ of Lebesgue measure zero that contains, in every directio...

Cheng Chen, Jian-Bin Li, Long-Hui Li et al. · 0 citations

Preprint Oct 2026

Lebesgue measure of distance sets and $L^2$ ball inflation

We give an alternative proof of the $5/4$ result of Guth-Iosevich-Ou-Wang on the Falconer distance conjecture: if a compact set $E$ in the plane has Hausdorff dimension $>5/4$, then there exists $x\in E$ such that the pinned distance set $$\Delta_x(E):=\{|x-y|: y\in E\} $$ has positive Lebesgue measure. Moreover, we ar...

Sheng-Wen Gan, Bo-Cheng Liu, Shu-Kun Wu · 0 citations