Free boundary minimal surfaces with three boundary components

The symmetry and topology of a free boundary minimal surface in the Euclidean unit ball do not determine the surface uniquely. There exist infinitely many pairs of non-isometric free boundary minimal surfaces having the same genus $g$, three boundary components and antiprismatic symmetry group of order $4(g+1)$.

References

• A. Carlotto, M. B. Schulz and D. Wiygul, Infinitely many pairs of free boundary minimal surfaces with the same topology and symmetry group, Memoirs of the AMS (to appear).
• N. Kapouleas and M. Li, Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disc, J. Reine Angew. Math. 776 (2021), 201–254.