Convexity and concavity of six-vertex phase interfaces

Let $q=1$, and impose stabilizing fixed boundary conditions producing an outer interface between the ferroelectric and disordered phases and an inner interface between the disordered and antiferroelectric phases. Interface-curvature conjecture. The outer interface is locally convex at every regular point, while the inner interface is locally concave at every regular point. This is presented as a conjecture about the general behavior of interfaces under stabilizing fixed boundary conditions; the source does not state a resolution.