Liouville theorems of subelliptic harmonic maps

In this paper, we discuss two Liouville-type theorems for subelliptic harmonic maps from sub-Riemannian manifolds to Riemannian manifolds. One is the Dirichlet version which states that two subelliptic harmonic maps from a sub-Riemannian manifold with boundary to a regular ball must be same if their restrictions on boundary are same; it is generalized to complete noncompact domains as well. The other is the vanishing-type theorem for finite L p -energy subelliptic harmonic maps on complete noncompact totally geodesic Riemannian foliations which are special sub-Riemannian manifolds.