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arXiv · 2504.18848

A reverse isoperimetric inequality for the Cheeger constant under width constraint

Ilias Ftouhi·Ilaria Lucardesi·Giorgio Saracco
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Abstract

Henrot and Lucardesi, in Commun. Contemp. Math. (2024), conjectured that among planar convex sets with prescribed minimal width, the equilateral triangle uniquely maximizes the Cheeger constant. In this short note, we confirm this conjecture. Moreover, we establish a stability result for the inequality in terms of the Hausdorff distance.

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Ilias Ftouhi, Ilaria Lucardesi, Giorgio Saracco. 2025-04-26. A reverse isoperimetric inequality for the Cheeger constant under width constraint. https://doi.org/10.1142/s0219199725501032

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