Liouville-type theorems for CC-harmonic maps from Riemannian manifolds to pseudo-Hermitian manifolds (Q2014338)

In the reviewed paper the authors consider a map \(f:(M,g)\to (N,H(N),J,\theta)\) from a Riemannian manifold to a pseudo-Hermitian manifold and introduce a horizontal energy functional \(E_H(f)\) for the map. The map \(f\) is called a Carnot-Caratheodory harmonic map, or CC-harmonic map for simplicity, if it is a critical point of \(E_H(f)\) with respect to any horizontal variational vector field. The authors also introduce the stress-energy tensor \(S_{f,H}\) associated with the horizontal energy \(E_H(f)\) which is a useful tool to investigate the conservation law of CC-harmonic maps. They investigate the monotonicity of CC-harmonic maps and establish the monotonicity formulae for the horizontal energy of CC-harmonic maps. Consequently, the authors obtain some Liouville-type theorems.