A reverse isoperimetric inequality for planar (α, β)-convex bodies

Gisella Croce (1) , Zakaria Fattah (2) , Giovanni Pisante (3)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre
2 ENSAM - Ecole Nationale Supérieure d'Arts et Métiers [Meknes]
3 Università degli studi della Campania "Luigi Vanvitelli"

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.

Domaines: Optimisation et contrôle [math.OC]

Gisella Croce, Zakaria Fattah, Giovanni Pisante. A reverse isoperimetric inequality for planar (α, β)-convex bodies. 2022. ⟨hal-03307914v5⟩