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arXiv · 1508.00643

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

Yunhui Wu
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Abstract

Let $S_g$ be a closed surface of genus $g$ and $\mathbb{M}_g$ be the moduli space of $S_g$ endowed with the Weil-Petersson metric. In this paper we investigate the Weil-Petersson curvatures of $\mathbb{M}_g$ for large genus $g$. First, we study the asymptotic behavior of the extremal Weil-Petersson holomorphic sectional curvatures at certain thick surfaces in $\mathbb{M}_g$ as $g \to \infty$. Then we prove two curvature properties on the whole space $\mathbb{M}_g$ as $g\to \infty$ in a probabilistic way.

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Yunhui Wu. 2015-08-04. On the Weil-Petersson curvature of the moduli space of Riemann surfaces of large genus. https://doi.org/10.1093/imrn%2Frnw053

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