The Kazdan-Warner problem on compact K\"ahler surfaces
Differential Geometry
2025-06-05 v3
Abstract
In this paper, we investigate a Kazdan-Warner problem on compact K\"ahler surfaces, which corresponds to prescribing sign-changing Chern scalar curvatures, and establish a Chen-Li type existence theorem on compact K\"ahler 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.
Keywords
Cite
@article{arxiv.2403.07698,
title = {The Kazdan-Warner problem on compact K\"ahler surfaces},
author = {Weike Yu},
journal= {arXiv preprint arXiv:2403.07698},
year = {2025}
}
Comments
14 pages. A revision has been made to the introduction, and add some remarks and an appendix