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, preprint (arXiv:2205.04861).
• 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.

genus = 2

genus = 2

genus = 3

genus = 3

genus = 4

genus = 4

genus = 7

genus = 7

genus = 11

genus = 11

genus = 15

genus = 15

genus = 19

genus = 19

genus = 27

genus = 27