A formula for the minimal perimeter of clusters with density (Q6082485)

Summary: This paper deals with the isoperimetric problem for clusters in a Euclidean space with double density. In particular, we show that a limit of an isoperimetric minimizing sequence of clusters with volumes \(\mathbf{V}\) is always isoperimetric for its own volumes (which may be smaller than \(\mathbf{V})\). In particular, if it is strictly smaller, we provide an explicit formula.