A note on the Chern-Yamabe flow on compact Hermitian manifolds with negative Gauduchon degree

Abstract

In this note, we prove that on a compact Hermitian manifold with negative Gauduchon degree, the Chern-Yamabe flow introduced in our recent work [13] converges to the solution of prescribed Chern scalar curvature problem, provided that the candidate curvature function is nonpositive and not identically zero.