Abstract
In this paper, we study holomorphic pairs over a class of non-compact Gauduchon manifolds. We prove that the stability implies the existence of Hermitian–Yang–Mills metric, and the semi-stability implies the existence of approximate Hermitian–Yang–Mills structure. We generalize the result in Bradlow (1991) [7] to the non-compact and non-Kähler case. Our proof is a combination of heat flow method and continuity method.
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