Most higher genus minimal surfaces with few symmetries require to solve complicated period problems. For very sophisticated examples see Martin Traizet’s paper below.
- Chen-Gackstatter surface of genus g
- Wohlgemuth’s surface of genus 2 with 4 ends
- Wohlgemuth’s surface of genus 3 with 4 ends
- Weber-Wolf surface of genus 3 with 5 ends
- Weber-Wolf surface of genus 4 with 5 ends
- Catenoid-Enneper of genus g
M. Traizet: Exploring the space of embedded minimal surfaces of finite total curvature. Experimental Mathematics 17, No 2, 205-221 (2008). See his web page for the preprint, images, and Maple work sheets.