On p -harmonic self-maps of spheres.

In this manuscript we study rotationally p -harmonic maps between spheres. We prove that for ( p ) given, there exist infinitely many p -harmonic self-maps of S m for each m ∈ N with p < m < 2 + p + 2 p . In the case of the identity map of S m we explicitly determine the spectrum of the corresponding Jacobi operator and show that for p > m , the identity map of S m is equivariantly stable when interpreted as a p -harmonic self-map of S m .