  It is shown that any three-dimensional periodic configuration that is
strictly stable for the area functional is exponentially stable for the surface
diffusion flow and for the Mullins-Sekerka or Hele-Shaw flow. The same result
holds for three-dimensional periodic configurations that are strictly stable
with respect to the sharp-interface Ohta-Kawaski energy. In this case, they are
exponentially stable for the so-called modified Mullins-Sekerka flow.
