Billiards in convex bodies with acute angles

Abstract

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 $K$.