Prescribed Chern scalar curvatures on complete noncompact Hermitian manifolds with nonpositive curvatures

In this paper, we investigate the problem of prescribing Chern scalar curvatures on complete noncompact Hermitian manifolds with nonpositive curvatures, and establish some existence results. In particular, we obtain some sufficient conditions for the existence of a constant negative Chern scalar curvature metric in the conformal class.