Singly Periodic Surfaces

There are many interesting singly periodic minimal surfaces. Particularly intricate are those invariant under a screw motion. By a theorem of Meeks and Rosenberg, embedded singly periodic minimal surfaces either have planar, annular (Scherk-type) or helicoidal ends.

Planar Ends

• Riemann
• Riemann with circles
• Callahan-Hoffman-Meeks
• Callahan-Hoffman-Meeks with added handles 1
• Callahan-Hoffman-Meeks with added handles 2

Annular (Scherk) Ends

• Scherk
• Scherk with non-orthogonal ends
• Scherk with more ends, most symmetric case
• Scherk with 6 ends
• Scherk with 8 ends
• Scherk with 10 ends
• Scherk with vertical handle

Helicoidal Ends

• Translation Invariant Helicoid
• Twisted Scherk with 4 ends
• Twisted Scherk with 6 ends, part 1
• Twisted Scherk with 6 ends, part 2
• Twisted Scherk with 8 ends
• Twisted Scherk with 10 ends
• Overtwisted Scherk with 4 ends

Other Ends

• Fence of Catenoids
• Catenoid with a broken handle
• Translation invariant k-Noids
• Screw Motion Invariant k-Noids
• Translation Invariant k-Noids with Handle
• Periodic k-Noid with annular ends
• Scherk with two ends twisted
• Wavy Helicoid
• Catalan's Surface

Animations

• Riemann
• Twisted Scherk with 4 ends
• Twisted Scherk with 8 ends