The Kazdan-Warner problem on compact Kähler surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913873258348544 |
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| author | Yu, Weike |
| author_facet | Yu, Weike |
| contents | 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 [Trans. Amer. Math. Soc. 347(1995) 1059-1066] on prescribing sign-changing Gaussian curvatures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07698 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Kazdan-Warner problem on compact Kähler surfaces Yu, Weike Differential Geometry 32Q15, 35J60 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 [Trans. Amer. Math. Soc. 347(1995) 1059-1066] on prescribing sign-changing Gaussian curvatures. |
| title | The Kazdan-Warner problem on compact Kähler surfaces |
| topic | Differential Geometry 32Q15, 35J60 |
| url | https://arxiv.org/abs/2403.07698 |