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

Parallel Ends with Wei type nodal limits

Parallel Ends with Scherk components

Numerical Examples (existence unproven)