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<p>In this paper, we investigate a Kazdan-Warner problem on compact Kähler surfaces, which corresponds to prescribing sign-changing Chern scalar curvatures, and establish a Chen-Li type existence theorem on compact Kähler surfaces when the candidate curvature function is of negative average. Moreover, we give an alternative proof of Ding-Liu’s theorem [5] on prescribing sign-changing Gaussian curvatures by using the sup+inf inequality due to H. Brezis, Y. Y. Li and I. Shafrir.</p>

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The Kazdan-Warner Problem on Compact Kähler Surfaces

  • 期刊论文

  • 发表日期：

    2026年5月22日

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  • Weike Yu

摘要

In this paper, we investigate a Kazdan-Warner problem on compact Kähler surfaces, which corresponds to prescribing sign-changing Chern scalar curvatures, and establish a Chen-Li type existence theorem on compact Kähler surfaces when the candidate curvature function is of negative average. Moreover, we give an alternative proof of Ding-Liu’s theorem [5] on prescribing sign-changing Gaussian curvatures by using the sup+inf inequality due to H. Brezis, Y. Y. Li and I. Shafrir.