Journal of Symplectic Geometry

Volume 20 (2022)

Number 1

On a systolic inequality for closed magnetic geodesics on surfaces

Pages: 99 – 134



Gabriele Benedetti (Mathematisches Institut, Ruprecht-Karls-Universität Heidelberg, Germany; and Department of Mathematics, Vrije Universiteit Amsterdam, The Netherlands)

Jungsoo Kang (Department of Mathematical Sciences, Research Institute in Mathematics, Seoul National University, Gwanak-Gu, Seoul, South Korea)


We apply a local systolic-diastolic inequality for contact forms and odd-symplectic forms on three-manifolds to bound the magnetic length of closed curves with prescribed geodesic curvature (also known as magnetic geodesics) on an oriented closed surface. Our results hold when the prescribed curvature is either close to a Zoll one or large enough.

Received 20 December 2019

Accepted 29 April 2021

Published 21 October 2022