Chun-Kit Lai

activity

20232025

collaborators

5 papers

math.CA2025

Fifty years of the Erdős similarity conjecture

Yeonwook Jung, Chun-Kit Lai, Yuveshen Mooroogen

Erdős similarity conjecture was proposed by P. Erdős in 1974. The conjecture remains open for exponentially decaying sequences as well as Cantor sets that have both Newhouse thickn…

math.MG2024

Interior of certain sums and continuous images of very thin Cantor sets

Yeonwook Jung, Chun-Kit Lai

We show that for all Cantor set $K_{1}$ on $R^{d}$ , it is always possible to find another Cantor set $K_{2}$ so that the sum $g (K_{1}) + K_{2}$ (where $g$ is a $C^{1}$ local diffeomor…

math.CA2024

Topological Erdős similarity conjecture and strong measure zero sets

Yeonwook Jung, Chun-Kit Lai

We resolve the topological version of the Erdős Similarity conjecture introduced previously by Gallagher, Lai and Weber. We show that a set is topologically universal on ${\mathbb…

math.CA2023

Erdős similarity problem via bi-Lipschitz embedding

De-jun Feng, Chun-Kit Lai, Ying Xiong

The Erdős similarity conjecture asserted that an infinite set of real numbers cannot be affinely embedded into every measurable set of positive Lebesgue measure. The problem is sti…

math.FA2023

Riesz bases of exponentials for multi-tiling measures

Chun-Kit Lai, Alexander Sheynis

Let $G$ be a closed subgroup of $R^{d}$ and let $ν$ be a Borel probability measure admitting a Riesz basis of exponentials with frequency sets in the dual group $G^{⊥}$ …