Published Paper

Inserted: 26 apr 2025
Last Updated: 27 oct 2025

Journal: Commun. Contemp. Math.
Year: 2025
Doi: 10.1142/S0219199725501032

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.

Keywords: Cheeger constant, Minimal width, reverse inequality

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• FLS-reverse-cheeger-minimal-width.pdf