Variational characterization of Lawson-band restrictions

Determine whether restrictions of the Lawson Möbius band \(\bar{\tau}_{1,2}\) to \(H_\lambda(C)\) solve a variational problem in the mean-convex handlebodies \(H_\lambda(C)\).

Background

The Lawson Möbius band is the principal candidate for the least-area and least-Willmore surface spanning the great circle. The paper asks whether its portions inside the mean-convex handlebodies arising by removing tubular neighborhoods of the circle have an analogous free-boundary variational characterization.

References

Do restrictions of the Lawson M\"obius band $\bar{\tau}{1,2}$ to $H\lambda(C)$ solve a variational problem in the mean convex handlebodies $H_\lambda(C)$?

— On the Willmore energy of Möbius bands  (2609.26745 - Bernstein et al., 22 Sep 2026) in Question 8.7, Section 8 (Problems)