2024/05/15 by Dong, Xianjing
#32H25 #32H30 #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2405.09659
We consider the classical Picard's problem for non-parabolic complete Kähler 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.