On Picard's Problem via Nevanlinna Theory

Abstract: We consider the classical Picard's problem for non-parabolic complete K\"ahler manifolds with non-negative Ricci curvature. Based on the global Green function approach, we give a positive answer to Picard's problem under certain condition by developing Nevanlinna theory. That is, we prove that every meromorphic function on such a manifold reduces to a constant if it omits three distinct values, provided that the manifold satisfies a volume growth condition.