Sums of sections, surface area measures, and the general Minkowski problem
Sums of sections, surface area measures, and the general Minkowski problem
For $2 \leq k \leq d - 1$, the $k$-th mean section body, $M_k(K)$, of a convex body $K$ in $\mathbb{R}^d$, is the Minkowski sum of all its sections by $k$-dimensional flats. We will show that the characterization of these mean section bodies is equivalent to the solution of the …