Concavity conjecture for the double-bubble profile in the three-torus

Let $T^3$ be the flat cubic three-torus, and for two prescribed volumes let $I(v_1,v_2)$ denote the least area required to enclose and separate those volumes.

Concavity conjecture. The least area to enclose and separate two given volumes in the three-torus is a concave function of the volumes.

The authors describe this as a deeper conjectural analogue of known concavity phenomena in Euclidean bubble problems. They establish only an elementary symmetry-related result toward it.