Prescribing Chern scalar curvatures on noncompact manifolds

In this paper, we investigate the noncompact prescribed Chern scalar curvature problem which reduces to solve a Kazdan-Warner type equation on noncompact non-Kahler manifolds. By introducing an analytic condition on noncompact manifolds, we establish related existence results. As its another application, we further give a new geometric proof of a classical multiplicity theorem of Ni (1982) [28]. (c) 2024 Elsevier Inc. All rights reserved.