On the finiteness of meromorphic mappings from a complete Kähler manifold into complex projective spaces

In this paper, we prove some general results on the finiteness of meromorphic mappings of a complete Kähler manifold whose universal covering is biholomorphic to a ball in \({\mathbb {C}}^m\) ${\mathbb{C}}^m$ into \({\mathbb {P}}^n({\mathbb {C}})\) ${\mathbb{P}}^n(\mathbb{C})$ sharing hyperplanes in general position with truncated multiplicities to level p ( \(1\le p\le n\) $1\le p\le n$ ).