## Free boundary minimal surfaces in ellipsoids

In the Euclidean unit ball, the equatorial disc is *unique* in the class of immersed free boundary minimal discs [2].
In the '80s, Smyth [5, p. 411] raised the question whether or not free boundary minimal discs in Euclidean ellipsoids must also be *planar*.
This question remained unresolved for nearly four decades until the discovery of several types of *nonplanar* free boundary minimal discs in ellipsoids [1,3,4].
Moreover, any ellipsoid contains at least three distinct free boundary minimal annuli [4].

### References

- R. Haslhofer and D. Ketover,
*Free boundary minimal disks in convex balls.*Preprint (arXiv:2307.01828). - J. C. C. Nitsche,
*Stationary partitioning of convex bodies.*Arch. Rational Mech. Anal. 89 (1985), 1–19. - R. Petrides,
*Non planar free boundary minimal disks into ellipsoids.*Preprint (arXiv:2304.12111). - M. B. Schulz,
*Equivariant free boundary minimal discs and annuli in ellipsoids.*Preprint (arXiv:2406.13465). - B. Smyth,
*Stationary minimal surfaces with boundary on a simplex.*Invent. Math. 76 (1984), 411–420.

free boundary minimal disc

free boundary minimal disc

containing the $x$-axis

containing the $x$-axis

free boundary minimal disc

containing the $x$- and $z$-axes

containing the $x$- and $z$-axes

free boundary minimal annulus around the $x$-axis

free boundary minimal annulus around the $y$-axis

free boundary minimal annulus around the $z$-axis