On p-harmonic self-maps of spheres

Abstract

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 mathbb {S}^m for each min mathbb {N} with p<m< 2+p+2sqrt{p}. In the case of the identity map of mathbb {S}^m we explicitly determine the spectrum of the corresponding Jacobi operator and show that for p>m, the identity map of mathbb {S}^m is equivariantly stable when interpreted as a p-harmonic self-map of mathbb {S}^m.