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math.SG2017★ 9 cited
Systolic ratio, index of closed orbits and convexity for tight contact forms on the three-sphere
Alberto Abbondandolo, Barney Bramham, Umberto Hryniewicz +1
We construct a dynamically convex contact form on the three-sphere whose systolic ratio is arbitrarily close to 2. This example is related to a conjecture of Viterbo, whose validit…
math.SG2017
Contact forms with large systolic ratio in dimension three
Alberto Abbondandolo, Barney Bramham, Umberto L. Hryniewicz +1
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…