A note on Hermitian-Einstein metrics on parabolic stable bundles

Abstract

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