The Prescribed Chern Scalar Curvature Problem

Abstract The paper is an attempt to resolve the prescribed Chern scalar curvature problem. We look for solutions within conformal class of a fixed Hermitian metric. divide problem in three cases, according sign Gauduchon degree, that we analyse separately. In case where degree negative, prove every non-identically zero and non-positive function unique metric one. Moreover, if there exists balanced with curvature, smooth changing negative mean value