On p-harmonic self-maps of spheres

The paper proves the existence of infinitely many O(m)-equivariant p-harmonic self-maps of S^m in the sharp window p < m < p + 2 + 2√p, and shows nonexistence beyond it. The candidate reproduces most of the reduction, reparametrization, Lyapunov monotonicity, oscillation, and shooting strategy. However, the candidate overclaims a stronger result—existence for every degree k ≥ 1—whereas the paper only establishes infinitely many solutions (as in the harmonic case, these correspond to families of degrees 0 and/or 1, not arbitrary degree k). This degree claim is unsupported by the paper’s construction and conflicts with the orbit-limit analysis used in the proof.