I. Ftouhi - I. Lucardesi - G. Saracco
A reverse isoperimetric inequality for the Cheeger constant under width constraint
Submitted Paper
Inserted: 26 apr 2025
Last Updated: 29 apr 2025
Year: 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.
Keywords: Minimal width, Cheeger constan, reverse inequality
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