Doubly Periodic

A minimal surface is doubly periodic if it is invariant under two linearly independent translations (but not three). To be embedded, it needs to have annular ends (also called Scherk ends) that are asymptotic to half planes.

• Non-parallel annular top and bottom ends
  • Scherk’s Doubly Periodic Surface
  • The Doubly Periodic Karcher-Scherk Surface of Genus One
  • Doubly Periodic Karcher-Scherk Surfaces of Higher Genus
  • Tilted Scherk Surfaces
• Parallel top and bottom ends
  • Genus 1
    • Karcher-Meeks-Rosenberg surfaces
  • Genus 2
    • Wei’s genus 2 surface
    • Rossman-Thayer-Wohlgemuth M1+
    • A less symmetric genus 2 surface
  • Genus 3
    • Rossman-Thayer-Wohlgemuth M1+-
    • Lübeck-Batista Surface of genus 3
    • Another Doubly Periodic CHM Surface
    • Limit of triply periodic g=5 (++|+-)b surface
    • Connor’s Experimental Surfaces of genus 3
  • Higher Genus
    • Higher Genus Wei Surfaces
    • Other higher genus examples
• Exotic ends
  • Plane with Catenoids
  • Doubly Periodic Catenoid