  We establish a new symmetrization procedure for the isoperimetric problem in
symmetric spaces of noncompact type. This symmetrization generalizes the well
known Steiner symmetrization in euclidean space. In contrast to the classical
construction the symmetrized domain is obtained by solving a nonlinear elliptic
equation of mean curvature type. We conclude the paper discussing possible
applications to the isoperimetric problem in symmetric spaces of noncompact
type.
