## Free boundary minimal surfaces of genus zero

equatorial disc

critical catenoid

3 boundary components

4 boundary components

5 boundary components

6 boundary components

4 boundaries around the vertices of a

tetrahedron

tetrahedron

6 boundaries around the vertices of an

octahedron

octahedron

8 boundaries around the vertices of a

hexahedron

hexahedron

12 boundaries around the vertices of an

icosahedron

icosahedron

20 boundaries around the vertices of a

dodecahedron

dodecahedron

32 boundaries around the vertices of a

pentakisdodecahedron (Conjecture)

pentakisdodecahedron (Conjecture)

### References

- A. Fraser and R. Schoen,
*Sharp eigenvalue bounds and minimal surfaces in the ball*, Invent. Math. 203 (2016), 823–890. - D. Ketover,
*Free boundary minimal surfaces of unbounded genus*, preprint (arXiv:1612.08691).