  We establish sufficient conditions for a function on the torus to be equal to
its Steiner symmetrization and apply the result to volume-constrained
minimizers of the Cahn-Hilliard energy. We also show how two-point
rearrangements can be used to establish symmetry for the Cahn-Hilliard model.
In two dimensions, the Bonnesen inequality can then be applied to
quantitatively estimate the sphericity of superlevel sets.
