Nevanlinna theory for meromorphic maps from a closed submanifold of ${\mathbb{C}}^l$ to a compact complex manifold

Abstract

The purpose of this article is threefold. The first is to construct a Nevanlina theory for meromorphic mappings from a polydisc to a compact complex manifold. In particular, we give a simple proof of Lemma on logarithmic derivative for nonzero meromorphic functions on ${\mathbb{C}}^l.$ The second is to improve the definition of the non-integrated defect relation of H. Fujimoto \cite{F2} and to show two theorems on the new non-integrated defect relation of meromorphic maps from a closed submanifold of ${\mathbb{C}}^l$ to a compact complex manifold. The third is to give a unicity theorem for meromorphic mappings from a Stein manifold to a compact complex manifold.

arXiv commentThe proof of the main result of this paper is not correct. We cannot rectify it. So we would like to withdraw it