Semi-conformal polynomials and harmonic morphisms

We prove a Liouville type theorem for harmonic morphisms from R-m to R-n (n greater than or equal to 3), showing that any such mapping which is defined off a polar set must be polynomial. We show that any semi-conformal mapping from R-m to R-n defined by polynomials is necessarily harmonic. This result has consequences for the local behaviour of a semi-conformal mapping between arbitrary Riemannian manifolds about a singular point.