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. 
Shiri Artstein-Avidan, Yaron Ostrover
math.SG math.DG