Body of constant width with minimal area in a given annulus
Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 415-438.

In this paper we address the following shape optimization problem: find the planar domain of least area, among the sets with prescribed constant width and inradius. In the literature, the problem is ascribed to Bonnesen, who proposed it in [3]. In the present work, we give a complete answer to the problem, providing an explicit characterization of optimal sets for every choice of width and inradius. These optimal sets are particular Reuleaux polygons.

Dans cet article nous étudions le problème d’optimisation de forme : trouver le domaine plan d’aire minimale parmi les convexes de largeur constante et d’inradius donnés. Dans la littérature, ce problème est attribué à Bonnesen qui a proposé une conjecture pour le domaine optimal. Nous donnons ici une réponse complète à ce problème en décrivant les domaines optimaux pour tout choix de la largeur et de l’inradius. Ces domaines sont des polygones de Reuleaux particuliers.

Received:
Accepted:
Published online:
DOI: 10.5802/jep.150
Classification: 52A10,  49Q10,  49Q12,  52A38
Keywords: Area minimization, constant width, inradius constraint, Reuleaux polygons
Antoine Henrot 1; Ilaria Lucardesi 1

1 Université de Lorraine CNRS, IECL F-54000 Nancy, France
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Antoine Henrot; Ilaria Lucardesi. Body of constant width with minimal area in a given annulus. Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 415-438. doi : 10.5802/jep.150. https://jep.centre-mersenne.org/articles/10.5802/jep.150/

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