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Prescribed Chern scalar curvature flow on compact Hermitian manifolds with negative Gauduchon degree (2501.03570v1)
Published 7 Jan 2025 in math.DG
Abstract: In this paper, we present a unified flow approach to prescribed Chern scalar curvature problem on compact Hermitian manifolds with negative Gauduchon degree. When the conformal class of its Hermitian metric contains a balanced metric, we give some sufficient conditions on the candidate curvature function $f$ which guaranties the convergence of the flow to a conformal Hermitian metric whose Chern scalar curvature is $f$.