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New results on the geometry of the moduli space of Riemann surfaces

Kefeng Liu XiaoFeng Sun Shing-Tung Yau

Differential Geometry mathscidoc:1912.43098

Science in China Series A: Mathematics, 51, (4), 632-651, 2008.4
We briefly survey our recent results about the Mumford goodness of several canonical metrics on the moduli spaces of Riemann surfaces, including the Weil-Petersson metric, the Ricci metric, the Perturbed Ricci metric and the Kahler-Einstein metric. We prove the dual Nakano negativity of the Weil-Petersson metric. As applications of these results we deduce certain important results about the <i>L</i> <sup>2</sup>-cohomology groups of the logarithmic tangent bundle over the compactified moduli spaces.
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@inproceedings{kefeng2008new,
  title={New results on the geometry of the moduli space of Riemann surfaces},
  author={Kefeng Liu, XiaoFeng Sun, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111527695231658},
  booktitle={Science in China Series A: Mathematics},
  volume={51},
  number={4},
  pages={632-651},
  year={2008},
}
Kefeng Liu, XiaoFeng Sun, and Shing-Tung Yau. New results on the geometry of the moduli space of Riemann surfaces. 2008. Vol. 51. In Science in China Series A: Mathematics. pp.632-651. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111527695231658.
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