Estimates for the average scalar curvature of the Weil-Petersson metric on the Moduli space $\overline{\cal M}_g$

TL;DR

This paper provides a detailed estimate of the average scalar curvature of the Weil-Petersson metric on the moduli space of curves as the genus grows large, up to order 1/g^2.

Contribution

It offers the first precise asymptotic estimate for the average scalar curvature of the Weil-Petersson metric on moduli spaces as genus increases.

Findings

Average scalar curvature estimate up to order 1/g^2

Asymptotic behavior of the Weil-Petersson metric

Insights into moduli space geometry at large genus

Abstract

We give a precise estimate for the average scalar curvature of the Weil-Petersson metric on the moduli space $\overline{\cal M}_g$ as $g\to\infty$ up to the order $1/g^2$.