Singly Periodic

Singly periodic minimal surfaces are in the simplest case invariant under a translation, or more generally, under a screw motion. Possible embedded ends can be planar, annular, or helicoidal.

• Annular Ends:
  • Scherk’s Singly Periodic Surface
  • Symmetrized Scherk Surface
  • Toroidal Karcher-Scherk Surfaces
  • 6-ended Scherk (g=0)
  • 6-ended Scherk (g=1)
  • Costa-Scherk Surface (g=1)
  • 8-ended Scherk (g=2)
  • daSilva-Batista Surface (g=2, 8 ends)
  • Translation Invariant Fischer-Koch Surfaces
• Helicoidal Ends:
  • The Helicoid
  • Helicoidal Karcher-Scherk Surfaces
  • Helicoidal Fischer-Koch Surfaces
  • Fischer-Koch-Freese Surfaces
• Planar Ends
  • Riemann’s Minimal Surface
  • Callahan-Hoffman-Meeks Surfaces
  • Screw-Motion Invariant CHM Surfaces
  • Higher Genus Surfaces with Planar Ends (Freese)
• Catenoidal Ends
  • Translation Invariant Catenoid
  • Translation Invariant Catenoid with a Handle
  • Translation Invariant Catenoid with Two Handles
  • Translation Invariant Plane with Catenoids
  • Hackman Surfaces
• Periodic Enneper Ends
  • Catalan’s Surface
  • Translation Invariant Enneper Surface
  • Scherk-Enneper Surfaces
• Mixed Ends:
  • The Half-Twisted Scherk Surface
  • Translation Invariant Costa Surface I