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).
