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arXiv · 2107.14455

A reverse isoperimetric inequality for planar ($\alpha$, $\beta$)--convex bodies

Gisella Croce·Zakaria Fattah·Giovanni Pisante
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Abstract

In this paper, we study a reverse isoperimetric inequality for planar convex bodies whose radius of curvature is between two positive numbers 0 < $\alpha$ < $\beta$, called ($\alpha$, $\beta$)--convex bodies. We show that among planar ($\alpha$, $\beta$)--convex bodies of fixed perimeter, the extremal shape is a domain whose boundary is composed by two arcs of circles of radius $\alpha$ joined by two arcs of circles of radius $\beta$.

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Gisella Croce, Zakaria Fattah, Giovanni Pisante. 2021-07-30. A reverse isoperimetric inequality for planar ($\alpha$, $\beta$)--convex bodies. https://arxiv.org/abs/2107.14455

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