A reverse isoperimetric inequality for the Cheeger constant under width constraint
Optimization and Control
2025-11-18 v2
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
Cite
@article{arxiv.2504.18848,
title = {A reverse isoperimetric inequality for the Cheeger constant under width constraint},
author = {Ilias Ftouhi and Ilaria Lucardesi and Giorgio Saracco},
journal= {arXiv preprint arXiv:2504.18848},
year = {2025}
}
Comments
17 pages, 1 figure