Minimal surfaces are defined as being locally minimal: the local least area definition of TPMS is defined in terms of minimizing the local area of at each point in the surface.

However, it is also sometimes claimed that the surface area of TPMS is a local minimum to the surface area function, which does not seem to be the case.

For example, the Schwartz Primitive `cos x + cos y + cos z = i` has a larger area for `i=0` then `i=e` for a small value of e.

Is it incorrect to say that TPMS are a local optimum w.r.t. surface minimization?

Does this mean that in physical reality soap bubbles which are constrained to polyhedra won't be able to keep a steady TPMS shape?