Liouville type currents for holomorphic maps. (Q1565877)

It is shown: every regularized positiv closed current \(T\) with slow growth on a Kähler manifold \(M\) is a Liouville current with respect to the class of holomorphic maps bounded on the support of \(T\) with values on a Kähler manifold \(N\) whose Kähler form is exact. A Cassorati-Weierstrass type theorem [see \textit{K. Takegoshi}, J. Math. Soc. Japan 45, No. 2, 301-311 (1993; Zbl 0788.32004)] and conditions when a complete Kähler manifold \(M\) with nonnegative Ricci curvature at infinity can be a Liouville type are established.