A local contact systolic inequality in dimension three
Gabriele Benedetti
Universität Heidelberg, GermanyJungsoo Kang
Seoul National University, South Korea
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Abstract
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.
Cite this article
Gabriele Benedetti, Jungsoo Kang, A local contact systolic inequality in dimension three. J. Eur. Math. Soc. 23 (2021), no. 3, pp. 721–764
DOI 10.4171/JEMS/1022