A note on Kähler manifolds of nonnegative holomorphic bisectional curvature (Q793999)

Let M be a Kähler manifold and D be a relatively compact domain of M with smooth boundary \(\partial D\). In this paper the author obtains some necessary and sufficient conditions such that D is a Stein manifold in terms of the holomorphic bisectional curvature of M on D and the second fundamental form of \(\partial D\). Also he proves: If M is a Kähler manifold of non-negative holomorphic bisectional curvature, then M has no exceptional set in the sense of Grauert. If there is a proper holomorphic map \(\tau: M\to \bar M\) from M onto a complex manifold \(\bar M\) such that \(\tau\) is biholomorphic on an open dense subset of M, then \(\tau\) is globally biholomorphic on M.