JournalsjemsVol. 23 / No. 3DOI 10.4171/jems/1022

A local contact systolic inequality in dimension three

  • Gabriele Benedetti

    Universität Heidelberg, Germany
  • Jungsoo Kang

    Seoul National University, South Korea
A local contact systolic inequality in dimension three cover

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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.