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Khler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities

Xiuxiong Chen Simon Donaldson SONG SUN

Differential Geometry mathscidoc:1912.43449

Journal of the American Mathematical Society, 28, (1), 183-197, 2015
This is the first of a series of three papers which prove the fact that a K-stable Fano manifold admits a Khler-Einstein metric. The main result of this paper is that a Khler-Einstein metric with cone singularities along a divisor can be approximated by a sequence of smooth Khler metrics with controlled geometry in the Gromov-Hausdorff sense.
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@inproceedings{xiuxiong2015khler-einstein,
  title={Khler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities},
  author={Xiuxiong Chen, Simon Donaldson, and SONG SUN},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114519495494009},
  booktitle={Journal of the American Mathematical Society},
  volume={28},
  number={1},
  pages={183-197},
  year={2015},
}
Xiuxiong Chen, Simon Donaldson, and SONG SUN. Khler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities. 2015. Vol. 28. In Journal of the American Mathematical Society. pp.183-197. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114519495494009.
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