Billiards in convex bodies with acute angles

In this paper we investigate the existence of closed billiard trajectories in not necessarily smooth convex bodies. In particular, we show that if a body $K\subset \mathbb{R}^d$ has the property that the tangent cone of every non-smooth point $q\in \partial K$ is acute (in a certain sense) then there is a closed billiard trajectory in $K$.