PreprintCC BY-NC-SA 4.0arXiv
Isoperimetric Inequalities in the ℓ∞ cube and torus
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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BibTeX
@misc{baker2026isoperimetric,
title = {{Isoperimetric Inequalities in the $\ell_\infty$ cube and torus}},
author = {Ben Baker and Joseph Briggs and Manuel Fernandez V and Chris Wells},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22456},
eprint = {2609.22456},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22456},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Isoperimetric Inequalities in the ℓ_∞ cube and torus
AU - Ben Baker
AU - Joseph Briggs
AU - Manuel Fernandez V
AU - Chris Wells
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22456
UR - https://arxiv.org/abs/2609.22456
AB - 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.
ER -