Is there anything resembling differential calculus over the space of (nicely behaved) regions in $\mathbb{R}^d$, where addition is interpreted in terms of Minkowski sums? For example, it is known that Minkowski sums act linearly on the perimeter of two-dimensional convex bodies. Is there any sense in which one could define something like a (constant) gradient for the perimeter function? I would assume that if anything, said gradient would just be a circle centered at the origin.