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arXiv · 2608.14454

The Erdős distinct distances problem in $\mathbb{R}^3$

Jonathan Tidor·Hung-Hsun Hans Yu·Dmitrii Zakharov
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Abstract

We prove that $N$ points in $\mathbb{R}^3$ determine at least $N^{2/3-o(1)}$ distinct distances.

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Jonathan Tidor, Hung-Hsun Hans Yu, Dmitrii Zakharov. 2026-08-14. The Erdős distinct distances problem in $\mathbb{R}^3$. https://arxiv.org/abs/2608.14454

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