On Picard's Theorem Via Nevanlinna Theory

We study a long-standing Picard's problem for non-compact complete K\"ahler manifolds with non-negative Ricci curvature. When the manifold carries a positive Green function, a positive answer is given to the Picard's problem, i.e., it is showed that every meromorphic function on such a manifold reduces to a constant if it omits three distinct values.