On locally biholomorphic finitely valent mappings from multi-connected domains onto the open disc

In this paper we offer new results of research presented in the referred papers of J.E. Fornaess and E.L. Stout, E. Ligocka and the authors, and concerning the existence of m-valent locally biholomorphic mappings from product domains of C n onto n-dimensional complex manifolds. In particular, we confirm an own conjecture about the estimation of the valentness m of locally biholomorphic mappings from multi-connected domains onto the open unit disc.