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

Abstract

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.