Communications in Analysis and Geometry
Volume 25 (2017)
Scalar curvatures of Hermitian metrics on the moduli space of Riemann surfaces
Pages: 465 – 484
In this article we show that any finite cover of the moduli space of closed Riemann surfaces of $g$ genus with $g \geqslant 2$ does not admit any complete finite-volume Hermitian metric of non-negative scalar curvature. Moreover, we also show that the total mass of the scalar curvature of any almost Hermitian metric, which is equivalent to the Teichmüller metric, on any finite cover of the moduli space is negative provided that the scalar curvature is bounded from below.
moduli space, scalar curvature, Teichmüller metric
2010 Mathematics Subject Classification
Paper received on 30 April 2015.