A discrete variational problem related to Ising droplets at low temperatures

We consider a variational problem on thed-dimensional latticeZ^d which has applications in the study of the meatastable behavior of the stochastic Ising model. The problem, an isoperimetric one, is to find what is the smallest area a finite subset ofZ^d can have restricted to three classes of subsets ofZ^d. If is one of these subsets, we define its volume as the number of points in it and its area as the number of pairs of points inZ^d which are neighbors and such that only one of them belongs to .