Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds - Deng, Fusheng; Ning, Jiafu; Wang, Zhiwei; Zhou, Xiangyu (Comptes Rendus. Mathématique)
We show that a singular Hermitian metric on a holomorphic vector bundle over a Stein manifold which is negative in the sense of Griffiths (resp. Nakano) can be approximated by a sequence of smooth Hermitian metrics with the same curvature negativity. We also show that a smooth Hermitian metric on a holomorphic vector bundle over a Stein manifold restricted to a submanifold which is negative in the sense of Griffiths (resp. Nakano) can be extended to the whole bundle with the same curvature negativity.