Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 23 | |
Number of page(s) | 40 | |
DOI | https://doi.org/10.1051/cocv/2024015 | |
Published online | 04 April 2024 |
Sharp inequalities involving the Cheeger constant of planar convex sets
1
Friedrich-Alexander-Universität Erlangen-Nürnberg, Department of Mathematics, Chair of Applied Analysis (Alexander von Humboldt Professorship),
Cauerstr. 11,
91058
Erlangen,
Germany
2
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Universita degli Studi di Napoli “Federico II”, Complesso Universitario Monte S. Angelo,
via Cintia,
80126
Napoli,
Italy
3
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Universita degli Studi di Napoli “Federico II”, Complesso Universitario Monte S. Angelo,
via Cintia,
80126
Napoli,
Italy
* Corresponding author: albalia.masiello@unina.it
Received:
22
June
2023
Accepted:
27
February
2024
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).
Mathematics Subject Classification: 52A10 / 52A40 / 65K15
Key words: Cheeger constant / convex sets / Blaschke-Santaló diagrams / sharp inequalities
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.