An integer parallelotope with small surface area

Assaf Naor; Oded Regev

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arXiv · 2301.02862

An integer parallelotope with small surface area

Assaf Naor·Oded Regev

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Abstract

We prove that for any $n\in \mathbb{N}$ there is a convex body $K\subseteq \mathbb{R}^n$ whose surface area is at most $n^{\frac12+o(1)}$, yet the translates of $K$ by the integer lattice $\mathbb{Z}^n$ tile $\mathbb{R}^n$.

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Assaf Naor, Oded Regev. 2023-01-07. An integer parallelotope with small surface area. https://arxiv.org/abs/2301.02862

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