Blaschke--Santal{ó} diagram for the volume, the diameter, and the Cheeger constant

We study the Blaschke--Santal{ó} diagram associated with the volume, the diameter, and the Cheeger constant. In the class of bounded open subsets of $\mathbb{R}^m$, $m\ge 2$, we give a complete description of the diagram. In the class of convex bodies of $\mathbb R^m$, we prove that the diagram is c