Ritoré–Ros isoperimetric conjecture for the cubic three-torus

Let $T^3$ be the flat cubic three-torus, and consider the isoperimetric problem of minimizing perimeter among regions of prescribed volume in $T^3$. The candidate minimizers are the sphere, cylinder, and slab.

Ritoré–Ros conjecture. The optima for the isoperimetric problem in a cubic $T^3$ are the sphere, cylinder, and slab.

This conjecture concerns the single-bubble problem underlying the double-bubble phase diagram. The source attributes it to Ritoré and Ros and presents it as an unresolved conjecture.