Estimates for the average scalar curvature of the Weil–Petersson metric on the moduli space $${\overline{{{\mathcal {M}}} }}_g$$

Abstract

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