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.
| Original language | English |
|---|---|
| Pages (from-to) | 99-134 |
| Number of pages | 36 |
| Journal | Journal of Symplectic Geometry |
| Volume | 20 |
| Issue number | 1 |
| Early online date | 21 Oct 2022 |
| DOIs | |
| Publication status | Published - 2022 |
Bibliographical note
Funding Information:Acknowledgements. This work was initiated when the authors worked together at the University of Münster and partially carried out while J.K. was affiliated with the Ruhr-University Bochum. We thank Peter Albers, Kai Zehmisch, and the University of Münster for having provided an inspiring academic environment. We are indebted to Stefan Suhr for the proof of ϵ(f) = sign(favg) for M ̸ T2 in Proposition 1.3 and to the anonymous referee for her/his suggestions that helped us improve the final version of the manuscript. G.B. would like to express his gratitude to Hans-Bert Rademacher and the whole Differential Geometry group at the University of Leipzig. G.B. is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC2181/1 - 390900948 (the Heidelberg STRUCTURES Excellence Cluster), under the Collaborative Research Center SFB/TRR 191 - 281071066 (Symplectic Structures in Geometry, Algebra and Dynamics) and under the Research Training Group RTG 2229 - 281869850 (Asymptotic Invariants and Limits of Groups and Spaces). J.K. is supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1801-01.
Publisher Copyright:
© 2022, International Press, Inc.. All rights reserved.