## 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).

genus 9 with 4 boundary components

genus 11 with 4 boundary components

genus 13 with 4 boundary components

## Free boundary analogues of the higher order Costaâ€“Wohlgemuth surfaces

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

genus 6 with 4 boundary components

genus 8 with 4 boundary components

genus 10 with 4 boundary components