A general comparison theorem for p-harmonic maps in homotopy class

We prove a general comparison result for homotopic finite p-energy C1 p-harmonic maps u,v:M→N between Riemannian manifolds, assuming that M is p-parabolic and N is complete and nonpositively curved. In particular, we construct a homotopy through constant p-energy maps, which turn out to be p-harmonic when N is compact. Moreover, we obtain uniqueness in the case of negatively curved N. This generalizes a well-known result in the harmonic setting due to R. Schoen and S.T. Yau.