Free boundary minimal surfaces of genus one

This family of free boundary minimal surfaces has a certain number of boundary components aligned along the equator and one catenoidal neck in the center, resulting in surfaces with genus one and large symmetry group. The extended family of free boundary minimal disc doublings also contains examples with genus one which only have two planes of symmetry.

References

• A. Folha, F. Pacard and T. Zolotareva, Free boundary minimal surfaces in the unit 3-ball, Manuscripta Math. 154 (2017), 359–409.
• G. Franz, D. Ketover and M. B. Schulz, Genus one critical catenoid, preprint (arXiv:2409.12588).