The study of variational questions associated to the area functional in weighted semi-Riemannian manifolds has been a focus of attention in the last years. In this direction, Rosales, Cañete, Bayle and Morgan investigated the isoperimetric problem for Euclidean space endowed with a continuous density, showing that, for a radial \(\log \) -convex density, balls about the origin are isoperimetric regions.