Free boundary minimal surfaces with four boundary components via doubling the critical catenoid

A doubling of the the critical catenoid can be glued to an embedded free boundary minimal surface with sufficiently large, odd genus and four boundary components.

References

• N. Kapouleas and P. McGrath, Generalizing the Linearized Doubling approach, I: General theory and new minimal surfaces and self-shrinkers. Camb. J. Math. 11 (2023).

Free boundary analogues of the higher order Costa–Wohlgemuth surfaces

Conjecturally, the Euclidean unit ball also contains free boundary minimal surfaces which look like the higher order Costa–Wohlgemuth surfaces, i.e. they have sufficiently large, even genus and four boundary components.