English

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

Differential Geometry 2018-01-19 v1 Analysis of PDEs

Abstract

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 Aut0(M,J)0Aut_0(M,J)\neq0. Moreover, we also show that when Aut0(M,J)0Aut_0(M,J)\neq0, the properness of KK-energy with respect to a suitably defined distance implies the existence of cscK.

Keywords

Cite

@article{arxiv.1801.05907,
  title  = {On the constant scalar curvature K\"ahler metrics, general automorphism group},
  author = {Xiuxiong Chen and Jingrui Cheng},
  journal= {arXiv preprint arXiv:1801.05907},
  year   = {2018}
}