Hermitian-Einstein metrics and Chern number inequalities on parabolic stable bundles over Kahler manifolds

Let (X) over bar be a compact complex manifold with a smooth Kahler metric and D = Sigma(i=1)(m) D-i a divisor in (X) over bar with normal crossings. Let E be a holomorphic vector bundle over (X) over bar with a stable parabo lic structure along D. We prove that there exists a Hermitian-Einstein metr ic on E' = E \(<(X)over bar\D) and obtain a Chern number inequality for a s table parabolic bundle. Without the assumption that the irreducible components D-i of D meet transv ersely, using Hironaka's theorem on the resolution of singularities, we als o get a Chern number inequality for a more general stable parabolic bundle.