Doubly Periodic Surfaces

Complete, embedded doubly periodic minimal have always anular ends which come, after rotating the surface, in top and bottom ones. All top ends and all bottom ends are necessarily parallel, but the top and bottom ends either make an angle or they don't. Strangely, this dichotomy seems to persists when a surface is deformed.

Non-Parallel Ends

• Scherk genus 0
• Scherk with handles
• Scherk with mixed handles

Parallel Ends with Wei type nodal limits

• Karcher-Meeks-Rosenberg genus 1, case a
• Karcher-Meeks-Rosenberg genus 1, case b
• Wei genus 2
• Rossman-Thayer-Wohlgmuth (case M1+-), genus 2
• Wei genus 3
• Wei genus 4
• Wei with mixed handles

Parallel Ends with Scherk components

• Connor's genus 2 surface
• Connor's genus 3 surface
• Connor's genus 9 surface

Numerical Examples (existence unproven)

• Asymmetric handle, genus 3
• Genus 4
• Connor genus 3 surface
• Connor's genus 9 surface

Non-Embedded

• Doubly Periodic Catenoids
• Conjugate of 4-Noid