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.
A reverse isoperimetric inequality for the Cheeger constant under width constraint / Ilias Ftouhi, Ilaria Lucardesi, Giorgio Saracco. - ELETTRONICO. - (2025), pp. 1-17.
A reverse isoperimetric inequality for the Cheeger constant under width constraint
Giorgio Saracco
2025
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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