Open books and the Weinstein conjecture
  We show the existence of a contractible periodic Reeb orbit for any contact structure supported by an open book whose binding can be realised as a hypersurface of restricted contact type in a subcritical Stein manifold. A key ingredient in the proof is a higher-dimensional version of Eliashberg's theorem about symplectic cobordisms from a contact manifold to a symplectic fibration. 
Max D\"orner, Hansj\"org Geiges and Kai Zehmisch
math.SG math.DS