It is known that given a stable holomorphic pair $(E,\phi)$, where $E$ is a holomorphic vector bundle on a compact Kähler manifold $X$ and $\phi$ is a holomorphic section of $E$, the vector bundle $E$ admits a Hermitian metric solving the vortex equation. We generalize this to pairs $(E,\phi)$, where $E$ is a reflexive sheaf on $X$.
"Vortex equation and reflexive sheaves." Adv. Theor. Math. Phys. 16 (2) 713 - 723, April 2012.