On Yang-Mills connections on compact K\"{a}hler surfaces

We extend an $L^2$-energy gap of Yang-Mills connections on principal $G$-bundles $P$ over a compact Riemannian manfold with a $good$ Riemannian metric to the case of a compact K"{a}hler surface with a $generic$ K"{a}hler metric $g$, which guarantees that all ASD connections on the principal bundle $P$ over $X$ are irreducible.