Bochen Liu

activity

20122022

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

3 citations · 4 across the 6 of their papers we have counts for

collaborators

Showing 2018Show all

4 papers · 1 filter

math.CA2018

Hausdorff dimension of pinned distance sets and the $L^{2}$ -method

Bochen Liu

We prove that for any $E \subset R^{2}$ , $dim_{H} (E) > 1$ , there exists $x \in E$ such that the Hausdorff dimension of the pinned distance set $$Δ_x(E)=\{|x-y|: y \in E\…

math.CO2018

Periodic structure of translational multi-tilings in the plane

Bochen Liu

Suppose $f \in L^{1} (R^{d})$ , $Λ \subset R^{d}$ is a finite union of translated lattices such that $f + Λ$ tiles with a weight. We prove that there exists a lattice $L\subse…

math.CO2018

Multi-tiling and equidecomposability of polytopes by lattice translates

Nir Lev, Bochen Liu

We characterize the polytopes in $R^{d}$ (not necessarily convex or connected ones) which multi-tile the space by translations along a given lattice. We also give a necessar…

math.CA2018

An $L^{2}$ -identity and pinned distance problem

Bochen Liu

Let $μ$ be a Frostman measure on $E \subset R^{d}$ . The spherical average decay $\int_{S^{d - 1}} ∣ μ (r ω) ∣^{2} d ω ≲ r^{- β}$ was originally used to attack Falconer…

Hausdorff dimension of pinned distance sets and the L2-method

Periodic structure of translational multi-tilings in the plane

Multi-tiling and equidecomposability of polytopes by lattice translates

An L2-identity and pinned distance problem

Hausdorff dimension of pinned distance sets and the $L^{2}$ -method

An $L^{2}$ -identity and pinned distance problem