On determination of convex bodies by their section functions

Alexander Fish, Dmitry Ryabogin, Wen Rui Sun +1

For a convex body $K$ its parallel section function in the direction $\theta \in S^{n-1}$ is defined by $$A_{K,θ}(t) = \mathrm{vol}_{n-1} \left( K \cap \{ x \in \mathbb{R}^n ~ | ~ \langl…