Infima of the Energy Functional in Homotopy Classes of Mappings of Complex Projective Space

We will determine the infimum of the energy in any homotopy class of mappings from complex projective space to a Riemannian manifold, 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 will also discuss some background and more general results involving geometric and topological influences on the infimum of the energy in a homotopy class and the properties of continuous, energy-minimizing maps.