A Note on Hermitian-Einstein Metrics on Parabolic Stable Bundles

Let $${\overline M}$$ be a compact complex manifold of complex dimension two with a smooth Kähler metric and D a smooth divisor on $${\overline M}$$. If E is a rank 2 holomorphic vector bundle on $${\overline M}$$ with a stable parabolic structure along D, we prove that there exista a Hermitian-Einstein metric on $$E\prime = E\vert_{{\overline M}\backslash D}$$ compatible with the parabolic structure, whose curvature is square integrable.