On the Weil-Petersson curvature of the moduli space of Riemann surfaces of large genus

Yunhui Wu Tsinghua University

Differential Geometry mathscidoc:1811.43003

Distinguished Paper Award in 2018

International Mathematics Research Notices,, 2017, (4), 2017
Let Sg be a closed surface of genus g and Mg be the moduli space of Sg endowed with the Weil–Petersson metric. In this article we investigate the Weil–Petersson curvatures of Mg for large genus g. First, we study the asymptotic behavior of the extremal Weil–Petersson holomorphic sectional curvatures at certain thick surfaces in Mg as g → ∞. Then we prove two curvature properties on the whole space Mg as g → ∞ in a probabilistic way.
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@inproceedings{yunhui2017on,
  title={On the Weil-Petersson curvature of the moduli space of Riemann surfaces of large genus},
  author={Yunhui Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181126095313218037180},
  booktitle={International Mathematics Research Notices,},
  volume={2017},
  number={4},
  year={2017},
}
Yunhui Wu. On the Weil-Petersson curvature of the moduli space of Riemann surfaces of large genus. 2017. Vol. 2017. In International Mathematics Research Notices,. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181126095313218037180.
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