Bochen Liu

activity

20122019

collaborators

4 papers

math.CA2019

Fourier frames for surface-carried measures

Alex Iosevich, Chun-Kit Lai, Bochen Liu +1

In this paper we show that the surface measure on the boundary of a convex body of everywhere positive Gaussian curvature does not admit a Fourier frame. This answers a question pr…

math.CA2017

Improvement on $2$ -chains inside thin subsets of Euclidean spaces

Bochen Liu

We prove that if the Hausdorff dimension of $E \subset R^{d}$ , $d \geq 2$ is greater than $\frac{d}{2} + \frac{1}{3}$ , the set of gaps of $2$ -chains inside $E$ , $$Δ_2(E)=\{(|x-y|…

math.CA2016

Equilateral triangles in subsets of $R^{d}$ of large Hausdorff dimension

Alex Iosevich, Bochen Liu

We prove that subsets of $R^{d}$ , $d \geq 4$ of large enough Hausdorff dimensions contain vertices of an equilateral triangle. It is known that additional hypotheses are needed…

math.CA2012

Optimal bounds for the Neuman-Sandor means in terms of geometric and contra-harmonic means

Tie-Hong Zhao, Yu-Ming Chu, Bo-Yu Liu

In this article, we prove that the double inequality $α G (a, b) + (1 - α) C (a, b) < M (a, b) < β G (a, b) + (1 - β) C (a, b)$ holds true for all $a, b > 0$ with $a \neq = b$ if and only if $α \geq 5/9$ and $β\…

Fourier frames for surface-carried measures

Improvement on 2-chains inside thin subsets of Euclidean spaces

Equilateral triangles in subsets of Rd of large Hausdorff dimension

Optimal bounds for the Neuman-Sandor means in terms of geometric and contra-harmonic means

Improvement on $2$ -chains inside thin subsets of Euclidean spaces

Equilateral triangles in subsets of $R^{d}$ of large Hausdorff dimension