English

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

R2 v1 2026-06-28T23:12:14.705Z