Inserted: 14 jun 2016
Last Updated: 17 feb 2017
Journal: Journal of Differential Geometry
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 en- ergy. In this case, they are exponentially stable for the so-called modified Mullins-Sekerka flow.