Bounds for Minkowski Billiard Trajectories in Convex Bodies

In this paper, we use the Ekeland–Hofer–Zehnder symplectic capacity to provide several bounds and inequalities for the length of the shortest periodic billiard trajectory in a smooth convex body in
$\mathbb R^n$
. Our results hold both for classical billiards, as well as for the more general case of Minkowski billiards.