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Abstract

We consider the classical Picard problem for non-parabolic complete Kähler manifolds with non-negative Ricci curvature. Based on a global Green function approach, we give an affirmative answer to this problem under certain conditions 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 whenever the manifold satisfies a volume growth condition; and prove that every meromorphic function of non-polynomial growth on such a manifold may avoid two distinct values at most.