Finsler geodesics, periodic Reeb orbits, and open books
  We survey some results on the existence (and non-existence) of periodic Reeb orbits on contact manifolds, both in the open and closed case. We place these statements in the context of Finsler geometry by including a proof of the folklore theorem that the Finsler geodesic flow can be interpreted as a Reeb flow. As a mild extension of previous results we present existence statements on periodic Reeb orbits on contact manifolds with suitable supporting open books. 
Max D\"orner, Hansj\"org Geiges, Kai Zehmisch
math.DS math.DG math.SG