Hofer–Zehnder capacity of flat Klein bottles

Determine the Hofer–Zehnder capacity of the unit disk cotangent bundle of a flat Klein bottle for arbitrary flat metrics.

Background

Flat Klein bottles are presented as a specific unresolved case within the broader problem of computing Hofer–Zehnder capacities for closed constant-curvature surfaces. The paper states that the capacity is not known in general, so even this geometrically structured nonorientable example remains incompletely understood.

References

Even for flat Klein bottles K, the capacity is unknown in general, while for closed orientable hyperbolic surfaces even its finiteness remains open [ABB+26].

— Hofer-Zehnder capacity as a geodesic selector  (2608.20177 - Bimmermann et al., 20 Aug 2026) in Section 1, page 3, paragraph beginning “Constant curvature”