| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 62 | |
| Number of page(s) | 18 | |
| DOI | https://doi.org/10.1051/cocv/2022056 | |
| Published online | 26 September 2022 | |
A reverse isoperimetric inequality for planar (α, β)-convex bodies
1
Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, 76600 Le Havre, France
2
Mathematics and Computer Science Department, ENSAM of Meknes, University of Moulay Ismail, Marjane II, AL Mansour, B.P. 15290, 50050 Meknes, Morocco
3
Dipartimento di Matematica e Fisica, Università degli Studi della Campania “Luigi Vanvitelli”, Viale Lincoln 5, 81100 Caserta, Italy
* Corresponding author: gisella.croce@univ-lehavre.fr
Received:
14
March
2022
Accepted:
24
August
2022
In this paper, we study a reverse isoperimetric inequality for planar convex bodies whose radius of curvature is between two positive numbers 0 ≤ α ≤ β, called (α, β)-convex bodies. We show that among planar (α, β)-convex bodies of fixed perimeter, the extremal shape is a domain whose boundary is composed by two arcs of circles of radius α joined by two arcs of circles of radius β.
Key words: Shape optimization / reverse isoperimetric inequality / Pontryagin maximum principle / convexity
© The authors. Published by EDP Sciences, SMAI 2022
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.
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