Torus equivariant harmonic maps between spheres

Abstract

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 π n+1(S n) (n⩾3) and of π n+2 ( S n ) ( n⩾5 odd) by harmonic maps, as well as infinitely many elements of π n(S n) (n∈ N ) . The existence proof involves equivariant regularity theory.