Yeonwook Jung

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math.CA2025

Interior of distance trees over thin Cantor sets

Yeonwook Jung, Krystal Taylor

It is known that if a compact set $E$ in $R^{d}$ has Hausdorff dimension greater than $(d + 1) /2$ , then its $n$ -chain distance set $$Δ^n(E) = \left\{\left(\left|x^1-x^2\right|…

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.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…