On a systolic inequality for closed magnetic geodesics on surfaces - Benedetti, Gabriele; Kang, Jungsoo (The journal of symplectic geometry, 2022)
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.