Magnetic billiards and the Hofer-Zehnder capacity of disk tangent bundles of lens spaces - Bimmermann, Johanna; Maier, Levin (Mathematische Annalen, 2025)
We compute the Hofer-Zehnder capacity of disk tangent bundles of certain lens spaces with respect to the round metric. Interestingly, we find that the Hofer-Zehnder capacity does not see the covering, i.e. the capacity of the disk tangent bundle of the lens space coincides with the capacity of the disk tangent bundle of the 3-sphere covering it. In particular, this gives a first example, where Gromov width and Hofer-Zehnder capacity of a disk tangent bundle disagree. We use techniques that include magnetic billiards for the lower bound and Gromov-Witten invariants for the upper bound.
Gesehen am 17.11.2025