## 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.

genus 2 with 3 boundary components

genus 2 with 3 boundary components

genus 4 with 3 boundary components

genus 4 with 3 boundary components

genus 7 with 3 boundary components

genus 7 with 3 boundary components

genus 11 with 3 boundary components

genus 11 with 3 boundary components

genus 15 with 3 boundary components

genus 15 with 3 boundary components

genus 19 with 3 boundary components

genus 19 with 3 boundary components

genus 27 with 3 boundary components

genus 27 with 3 boundary components