Spectral geometry of surfaces spanning a great circle

Determine whether there is a relationship between the theory of minimal surfaces spanning a great circle in \(\mathbb{S}^3\) and spectral geometry.

Background

The paper observes that coordinate functions of free-boundary minimal surfaces in the associated handlebodies are Steklov eigenfunctions. It asks whether this connection extends to a broader relationship between spectral geometry and minimal surfaces spanning the fixed great circle.