The canonical metric on holomorphic pairs over compact non-Kähler manifolds

In this paper, we prove the solvability of the vortex equation on a holomorphic vector bundle over a compact Hermitian manifold using the continuity method, and show the Kobayashi-Hitchin correspondence for holomorphic pairs. This work extends Bradlow's Kobayashi-Hitchin correspondence over compact Kähler manifolds to compact non-Kähler manifolds.