Determine whether the prismatic free boundary minimal surface constructions coincide

Determine whether the genus-zero free boundary minimal surfaces constructed by Folha, Pacard, and Zolotareva, Franz and Schulz, and Karpukhin, Kusner, McGrath, and Stern produce the same surfaces.

Background

The paper defines a class of embedded genus-zero free boundary minimal surfaces in the unit ball with prismatic symmetry, cyclically permuted boundary components, and equatorial reflection symmetry. It notes that this class contains the b-noids of Karpukhin, Kusner, McGrath, and Stern, the large-b surfaces of Folha, Pacard, and Zolotareva, and potentially the surfaces constructed by Franz and Schulz.

The constructions arise from different methods, including eigenvalue optimization, gluing, and min–max theory. The paper does not establish whether these apparently related examples are identical, so the relationship among the resulting surfaces remains unresolved.