A Note on Hermitian-Einstein Metrics on Parabolic Stable Bundles

Let M be a compact complex manifold of complex dimension two with a smooth Khler metric and D a smooth divisor on M. If E is a rank 2 holomorphic vector bundle on M with a stable parabolic structure along D, we prove that there exista a Hermitian-Einstein metric on E=E|MD compatible with the parabolic structure, whose curvature is square integrable.