Systolic criticality of the Lawson band

Determine whether the Lawson Möbius band \(\bar{\tau}_{1,2}\) has any criticality property with respect to systolic functionals on Möbius bands.

Background

The Lawson band is foliated by geodesic meridians, and the paper relates this geometry to known minimizers for systolic functionals on Möbius bands. It leaves unresolved whether the Lawson band is critical for any such systolic functional.