Nevanlinna theory on complete Kähler manifolds with non-negative Ricci curvature

Abstract

The paper develops an equidistribution theory of meromorphic mappings from a complete Kähler manifold with non-negative Ricci curvature into a complex projective manifold intersecting normal crossing divisors. When the domain manifolds are of maximal volume growth, one obtains a second main theorem with a refined error term. As a result, we prove a sharp defect relation in Nevanlinna theory. Furthermore, our results are applied to the propagation problems of algebraic dependence. As major consequences, we set up several unicity theorems for dominant meromorphic mappings on complete Kähler manifolds. In particular, we prove a five-value theorem on complete Kähler manifolds, which gives an extension of Nevanlinna's five-value theorem for meromorphic functions on $\mathbb{C}.$

arXiv commentThe article's main results have been overshadowed by another publication, see arXiv:2405.09659