We prove a general comparison result for homotopic finite p-energy C1p-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. © 2011 Elsevier Inc.
Veronelli, G. (2012). A general comparison theorem for p-harmonic maps in homotopy class. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 391(2), 335-349 [10.1016/j.jmaa.2011.03.037].
A general comparison theorem for p-harmonic maps in homotopy class
Veronelli, G
2012
Abstract
We prove a general comparison result for homotopic finite p-energy C1p-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. © 2011 Elsevier Inc.
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