Goodness of canonical metrics on the moduli space of Riemann surfaces

Kefeng Liu Xiaofeng Sun Shing-Tung Yau

Differential Geometry mathscidoc:1912.43109

Pure and Applied Mathematics Quarterly, 10, (2), 223-243, 2014.4
In this paper we will show the Mumford goodness of the metrics on the logarithmic tangent bundle of the moduli spaces of curves induced by the Ricci and the perturbed Ricci metrics. It follows from these estimates that the Ricci metric can be extended to the Deligne-Mumford compactification of the moduli spaces.
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@inproceedings{kefeng2014goodness,
  title={Goodness of canonical metrics on the moduli space of Riemann surfaces},
  author={Kefeng Liu, Xiaofeng Sun, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111609917471669},
  booktitle={Pure and Applied Mathematics Quarterly},
  volume={10},
  number={2},
  pages={223-243},
  year={2014},
}
Kefeng Liu, Xiaofeng Sun, and Shing-Tung Yau. Goodness of canonical metrics on the moduli space of Riemann surfaces. 2014. Vol. 10. In Pure and Applied Mathematics Quarterly. pp.223-243. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111609917471669.
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