Prescribed Chern scalar curvatures on compact Hermitian manifolds with negative Gauduchon degree

In this paper, we investigate the problem of prescribing Chern scalar curvatures on compact Hermitian manifolds with negative Gauduchon degree. By studying the convergence of the related geometric flow, we obtain some existence results when the candidate curvature function is nonzero and nonpositive. Furthermore, we also consider the case that the candidate curvature function is sign-changing, and establish some existence and nonexistence results. (c) 2023 Elsevier Inc. All rights reserved.