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

الأصل · EN

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 non-positively 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.