Sharp inequalities involving the Cheeger constant of planar convex sets

Ftouhi I, Masiello AL, Paoli G (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Esaim-Control Optimisation and Calculus of Variations EDP Sciences

Book Volume: 30

Article Number: 23

DOI: 10.1051/cocv/2024015

Abstract

We are interested in finding sharp bounds for the Cheeger constant h via different geometrical quantities, namely the area |€ ¢|, the perimeter P, the inradius r, the circumradius R, the minimal width w and the diameter d. We provide new sharp inequalities between these quantities for planar convex bodies and enounce new conjectures based on numerical simulations. In particular, we completely solve the Blaschke-Santaló diagrams describing all the possible inequalities involving the triplets (P, h, r), (d, h, r) and (R, h, r) and describe some parts of the boundaries of the diagrams of the triplets (w, h, d), (w, h, R), (w, h, P), (w, h, |€ ¢|), (R, h, d) and (w, h, r).

Authors with CRIS profile

Ilias Ftouhi Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Università degli Studi di Napoli Federico II IT Italy (IT)

How to cite

APA:

Ftouhi, I., Masiello, A.L., & Paoli, G. (2024). Sharp inequalities involving the Cheeger constant of planar convex sets. Esaim-Control Optimisation and Calculus of Variations, 30. https://doi.org/10.1051/cocv/2024015

MLA:

Ftouhi, Ilias, Alba Lia Masiello, and Gloria Paoli. "Sharp inequalities involving the Cheeger constant of planar convex sets." Esaim-Control Optimisation and Calculus of Variations 30 (2024).

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