Resumen de Contact forms with large systolic ratio in dimension three

Alberto Abbondandolo, Barney Bramham, Umberto Hryniewicz, Pedro A. S. Salomao

• The systolic ratio of a contact form on a closed three-manifold is the quotient of the square of the shortest period of closed Reeb orbits by the contact volume. We show that every co-orientable contact structure on any closed three-manifold is defined by a contact form with arbitrarily large systolic ratio.

  This shows that the many existing systolic inequalities in Finsler and Riemannian geometry are not purely contact-topological phenomena.