In this talk, we first derive the CR Bochner formula and the CR Kato’s inequality for pseudoharmonic maps. Secondly, by applying the CR Bochner formula and the CR Kato’s inequality we are able to prove the Liouville property for the pseudoharmonic maps with finite Dirichlet energy in a complete (2n+1)-pseudohermitian manifold. This is the CR analogue to the Liouville theorem for the harmonic maps in Riemannian geometry.   

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