Contact forms with large systolic ratio in dimension three
2019
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.
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