Torus equivariant harmonic maps between spheres

By minimizing in Sobolev spaces of mappings which are equivariant with respect to certain torus actions, we construct homotopically nontrivial harmonic maps between spheres. Doing so, we can represent the nontrivial elements of πn+1(Sn) (n⩾3) and of πn+2(Sn) (n⩾5 odd) by harmonic maps, as well as infinitely many elements of πn(Sn) (n∈N). The existence proof involves equivariant regularity theory.