Systolic Inequalities for S1-invariant Contact Forms

In contact geometry, a systolic inequality aims to give a uniform upper bound on the shortest period of a periodic Reeb orbit for contact forms with fixed volume on a given manifold. This generalizes a well-studied notion in Riemannian geometry. It is known that there is no systolic inequality valid for all contact forms on any given contact manifold. In this talk, I will state a systolic inequality for contact forms that are invariant under a circle action in dimension three.