  We determine the infimum of the energy in any homotopy class of mappings from
complex projective space to a Riemannian manifold, by showing that it is
proportional to the infimal area in the homotopy class of mappings of the
2-sphere represented by its action on the second homotopy group. We then
establish a family of optimal lower bounds, for mappings from real and complex
projective spaces to Riemannian manifolds, for a larger class of energy
functionals. We also give a new proof of a theorem of Ohnita that stable
harmonic mappings of complex projective spaces are pluriharmonic and establish
several properties of these maps.
