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arXiv · 1711.06544

Cube packings in Euclidean spaces

Han Yu
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Abstract

In this paper we study some cube packing problems. In particular we are interested in compact subsets of $\mathbb{R}^n,n\geq 2$, which contain boundaries of cubes with all side lengths in $(0,1)$. We show here that such sets must have lower box dimension at least $n-0.5$ and we will also provide sharp examples. We also show here that such sets must be large in general in a precise sense which is also introduced in this paper.

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Han Yu. 2017-11-17. Cube packings in Euclidean spaces. https://arxiv.org/abs/1711.06544

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