Kobayashi-Hitchin correspondence for tame harmonic bundles II

Let X be a smooth irreducible projective complex variety with an ample line bundle L, and D be a simple normal crossing hypersurface. We establish the Kobayashi-Hitchin correspondence between tame harmonic bundles on X D and mu(L)-stable parabolic lambda-flat bundles with trivial characteristic numbers on (X, D). In particular, we obtain the quasiprojective version of the Corlette-Simpson correspondence between flat bundles and Higgs bundles.