Wen-Rui Sun

On determination of convex bodies by their section functions

For a convex body $K$ its parallel section function in the direction $\theta\in S^{n-1}$ is defined by $$A_{K,\theta}(t) = \mathrm{vol}_{n-1} \left( K \cap \{ x \in \mathbb{R}^n ~ | ~ \langle x, \theta \rangle = t \} \right) .$$ We study to what extent the body $K$ is determined by partial information about these funct...