  Let $X$ be a normal compact K\"ahler variety, and $\mathcal{F}$ a coherent
reflexive sheaf on $X$. We investigate the existence of admissible Hermitian
metrics on $\mathcal{F}$. If moreover $\mathcal{F}$ is slope stable, we also
study the existence of admissible Hermitian-Yang-Mills metrics on it. The
existence will hold if one can prove a uniform Sobolev inequality on singular
spaces.
