On the constant scalar curvature K\"ahler metrics-general automorphism group

Xiuxiong Chen Stony Brook University Jingrui Cheng Stony Brook University

Analysis of PDEs arXiv subject: Differential Geometry (math.DG) mathscidoc:2005.03004

In this paper, we derive estimates for scalar curvature type equations with more singular right hand side. As an application, we prove Donaldson's conjecture on the equivalence between geodesic stability and existence of cscK when $Aut_0(M,J)\neq0$. Moreover, we show that when $Aut_0(M,J)\neq0$, the properness of $K$-energy with respect to a suitably defined distance implies the existence of cscK.
cscK metrics, general cscK type equations, apriori estimates
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@inproceedings{xiuxiongon,
  title={On the constant scalar curvature K\"ahler metrics-general automorphism group},
  author={Xiuxiong Chen, and Jingrui Cheng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200513040243012262675},
}
Xiuxiong Chen, and Jingrui Cheng. On the constant scalar curvature K\"ahler metrics-general automorphism group. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200513040243012262675.
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