This article is published open access under our Subscribe to Open model.
Let be a contact form on a connected closed three-manifold . The systolic ratio of is defined as , where and denote the minimal period of periodic Reeb orbits and the contact volume. The form is said to be Zoll if its Reeb flow generates a free -action on . We prove that the set of Zoll contact forms on locally maximises the systolic ratio in the -topology. More precisely, we show that every Zoll form admits a -neighbourhood in the space of contact forms such that for every , with equality if and only if is Zoll.