Fixed and periodic points of the intersection body operators of lower orders

Cheng Lin, Ge Xiong

For the intersection body operator of lower order $I_{i}K$ of a star body $K$ in ${\mathbb{R}}^n$, $i\in \{1,2,\dots ,n-2\}$, we prove that $I_i^{2}K=cK$ iff $K$ is an origin-symmetri…