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

2021/07/30 by Croce, Gisella, Fattah, Zakaria, Pisante, Giovanni
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2107.14455

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.

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