4 papers
math.CA2026
Some constructions of restricted Kakeya sets
Cheng Chen, Jianbin Li, Longhui Li +4
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…
math.CA2026
Lebesgue measure of distance sets with regular pins and multi-scale Mizohata-Takeuchi-type estimates
Bochen Liu
Suppose are Borel sets in the plane, , , and has equal Hausdorff and packing dimension. We prove tha…
math.CA2024
Orthogonal projection, dual Furstenberg problem, and discretized sum-product
Longhui Li, Bochen Liu
In this paper we come up with a dual version of the Furstenberg problem and obtain partial results via estimates of orthogonal projections. Examples are also discussed. Moreo…
math.CA2023
Falconer distance problem on Riemannian manifolds
Changbiao Jian, Bochen Liu, Yakun Xi
We prove that on a -dimensional Riemannian manifold, the distance set of a Borel set has a positive Lebesgue measure if $$\dim_{\mathcal{H}}(E)>\frac d2+\frac14+\frac{1-(-1)…