An integer parallelotope with small surface area

Assaf Naor, Oded Regev

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 $n^{\frac{1}{2}+o(1)}$, yet the translates of $K$ by the integer…