On p-harmonic maps into spheres

Abstract

We study the topology of p-harmonic maps ϕ : M →S^ν from a compact Riemannian manifold M into a sphere S^ν. We also show that any p-energy minimizing map ϕ : M → S^ν omitting a totally geodesic submanifold of codimension two Ε S^ν is of class C¹. This extends results by B. Solomon, [13], from harmonic to p-harmonic maps.