A reverse isoperimetric inequality for the Cheeger constant under width constraint
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 paper, we confirm this conjecture. Moreover, we establish a local stability result for the inequality in terms of the Hausdorff distance.
Authors
- Giorgio Saracco (ORCID: https://orcid.org/0000-0001-9675-2757)
- Ilias Ftouhi (ORCID: https://orcid.org/0000-0002-4681-7126)
- Ilaria Lucardesi (ORCID: https://orcid.org/0000-0003-1709-7876)
Institutions
- University of Pisa (IT)
- University of Ferrara (IT)
- Istituto Nazionale di Fisica Nucleare, Sezione di Pisa (IT)
- Université de Nîmes (FR)
Publication Details
- Journal
- Communications in Contemporary Mathematics
- Published
- 2025-10-24
- DOI
- https://doi.org/10.1142/s0219199725501032
- Primary Topic
- Point processes and geometric inequalities
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Alexander von Humboldt-Stiftung
- Istituto Nazionale di Alta Matematica "Francesco Severi"