On a systolic inequality for closed magnetic geodesics on surfaces

Abstract

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.

26 pages, a revised version of Part III in "A local systolic-diastolic inequality in contact and symplectic geometry" arXiv:1801.00539 (now withdrawn)

References in corpus (2)

• On a local systolic inequality for odd-symplectic forms
• A local contact systolic inequality in dimension three

Cited by in corpus (2)

• On a local systolic inequality for odd-symplectic forms
• A local contact systolic inequality in dimension three