Critical points of the multidimensional Dirichlet functional

The question of the existence of local minima is considered for the Dirichlet (energy) functional on spaces of mappings of one Riemannian manifold into another. In particular, it is shown that if the identity mapping of a compact irreducible homogeneous space onto itself has positive index, then any nonconstant harmonic mapping of an arbitrary compact orientable Riemannian manifold into such a space also has positive index.
Bibliography: 15 titles.