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arXiv · 2609.22456

Isoperimetric Inequalities in the $\ell_{\infty}$ cube and torus

Ben Baker·Joseph Briggs·Manuel Fernandez V·Chris Wells
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Abstract

We prove an exact isoperimetric inequality for cubes and tori under the $\ell_{\infty} metric. As a corollary, we recover the celebrated grid edge-isoperimetric inequality of Bollobás-Leader.

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Ben Baker, Joseph Briggs, Manuel Fernandez V, Chris Wells. 2026-09-18. Isoperimetric Inequalities in the $\ell_{\infty}$ cube and torus. https://arxiv.org/abs/2609.22456

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