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In this paper, we derive a sub-gradient estimate for pseudoharmonic maps fromnoncompact complete Sasakian manifolds which satisfy CR sub-Laplace comparisonproperty, to simply-connected Riemannian manifolds with nonpositive sectionalcurvature. As its application, we obtain some Liouville theorems forpseudoharmonic maps. In the Appendix, we modify the method and apply it toharmonic maps from noncompact complete Sasakian manifolds.

Liouville theorem for Pseudoharmonic maps from Sasakian manifolds