A MONOTONICITY FORMULA AND A LIOUVILLE TYPE THEOREM OF V-HARMONIC MAPS

Abstract

We establish a monotonicity formula of V -harmonic maps by using the stress-energy tensor. Use the monotonicity formula, we can derive a Liouville type theorem for V -harmonic maps. As applications, we also obtain monotonicity and constancy of Weyl harmonic maps from conformal manifolds to Riemannian manifolds and ±holomorphic maps between almost Hermitian manifolds. Finally, a constant boundary-value problem of V -harmonic maps is considered.