Prescribed Chern scalar curvatures on complete Hermitian manifolds

Published 17 Jun 2025 in math.DG | (2506.14592v2)

Abstract: In this paper, we investigate the problem of prescribing Chern scalar curvatures on complete Hermitian manifolds. Firstly, we re-prove our recent result for prescribing sign-changing Chern scalar curvatures on compact Hermitian manifolds by using the classical maximum principle. Secondly, we study this problem on complete noncompact Hermitian manifolds, and generalize the Aviles-McOwen's existence results [J. Differential Geom., 21 (1985): 269-281] from Poincar\'e disks to higher dimensional Hermitian manifolds.

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Authors (1)

Weike Yu

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