Bochen Liu

activity

20162020

most citedAn elementary approach to simplexes in thin subsets of Euclidean space

6 citations · 10 across the 3 of their papers we have counts for

collaborators

3 papers

math.CA2020★ 3 cited

Intersection between pencils of tubes, discretized sum-product, and radial projections

Bochen Liu, Chun-Yen Shen

In this paper we prove the following results in the plane. They are related to each other, while each of them has its own interest. First we obtain an $ε_{0}$ -increment on intersecti…

math.CA2019★ 1 cited

On Hausdorff dimension of radial projections

Bochen Liu

For any $x \in R^{d}$ , $d \geq 2$ , denote $π^{x} : R^{d} \ {x} \to S^{d - 1}$ as the radial projection $π^{x} (y) = \frac{y - x}{∣ y - x ∣} .$ Given a Borel set $E\sub…

math.CA2016★ 6 cited

An elementary approach to simplexes in thin subsets of Euclidean space

Allan Greenleaf, Alex Iosevich, Bochen Liu +1

We prove that if the Hausdorff dimension of $E \subset R^{d}$ , $d \geq 3$ , is greater than $min {\frac{d k + 1}{k + 1}, \frac{d + k}{2}},$ then the $(2 k + 1)$ -d…