A regularity result for shortest generalized billiard trajectories in convex bodies in $$\mathbb {R}^n$$
A regularity result for shortest generalized billiard trajectories in convex bodies in $$\mathbb {R}^n$$
We study length-minimizing closed generalized Euclidean billiard trajectories in convex bodies in $\mathbb{R}^n$ and investigate their relation to the inclusion minimal affine sections that contain these trajectories. We show that when passing to these sections, the length-minimizing closed billiard trajectories are still billiard trajectories, but their length-minimality as well as …