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V. ManuelFernandez

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Preprint Sep 2026

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

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 Bollob\'{a}s-Leader.

Ben Baker, J. Briggs, V. ManuelFernandez et al. · 0 citations
Preprint Aug 2026

Improved $\ell_0$-Isoperimetry for Convex Bodies via Mass Transport

We study $\ell_0$ isoperimetry for a convex body $K\subset \mathbb{R}^n$, $n\ge2$. For a Borel set $S\subset K$, let $\partial_0^K S$ be the set of points in $K \setminus S$ that can be reached from $S$ by changing at most one coordinate (i.e. the $\ell_0$ boundary of $S$). Suppose that, for some unconditional convex b...

V. ManuelFernandez · 0 citations

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