Symplectic capacities of disc cotangent bundles of flat tori

Abstract

We show that on the unit disc cotangent bundle of flat Riemannian tori, all normalized capacities coincide with twice the systole. The same result holds for flat, reversible Finsler tori and normalized capacities that are greater than or equal to the Hofer-Zehnder capacity.

arXiv comment6 pages. Comments are welcome! Fixed some typos. To appear in Proceedings of the AMS

References in corpus (6)

• From Symplectic Measurements to the Mahler Conjecture
• Symplectic embeddings and the lagrangian bidisk
• Symplectic embeddings into disk cotangent bundles
• Riemannian distance and symplectic embeddings in cotangent bundle
• Hofer-Zehnder capacity of disc tangent bundles of projective spaces
• Hofer-Zehnder capacity of magnetic disc tangent bundles over constant curvature surfaces

Cited by in corpus (2)

• Magnetic billiards and the Hofer-Zehnder capacity of disk tangent bundles of lens spaces
• Notes on symplectic squeezing in $T^{\ast }{\mathbb{T}}^n$ and spectra of Finsler dynamics