A reverse isoperimetric inequality for the Cheeger constant under width constraint

Ilias Ftouhi; Ilaria Lucardesi; Giorgio Saracco

doi:10.1142/S0219199725501032

A reverse isoperimetric inequality for the Cheeger constant under width constraint

Ilias Ftouhi, Ilaria Lucardesi, Giorgio Saracco^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 paper, we confirm this conjecture. Moreover, we establish a local stability result for the inequality in terms of the Hausdorff distance.

Original language	English
Article number	2550103
Journal	Communications in Contemporary Mathematics
DOIs	https://doi.org/10.1142/S0219199725501032
State	Accepted/In press - 2025
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2025 World Scientific Publishing Company.

Keywords

Cheeger constant
minimal width
reverse inequality

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1142/S0219199725501032

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title = "A reverse isoperimetric inequality for the Cheeger constant under width constraint",

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 paper, we confirm this conjecture. Moreover, we establish a local stability result for the inequality in terms of the Hausdorff distance.",

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author = "Ilias Ftouhi and Ilaria Lucardesi and Giorgio Saracco",

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year = "2025",

doi = "10.1142/S0219199725501032",

language = "English",

journal = "Communications in Contemporary Mathematics",

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T1 - A reverse isoperimetric inequality for the Cheeger constant under width constraint

AU - Ftouhi, Ilias

AU - Lucardesi, Ilaria

AU - Saracco, Giorgio

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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.

KW - Cheeger constant

KW - minimal width

KW - reverse inequality

UR - https://www.scopus.com/pages/publications/105021249423

U2 - 10.1142/S0219199725501032

DO - 10.1142/S0219199725501032

M3 - Article

AN - SCOPUS:105021249423

SN - 0219-1997

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

M1 - 2550103

ER -

A reverse isoperimetric inequality for the Cheeger constant under width constraint

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this