Remarks on invariant metrics on Teichmüller space

We make some comparisons concerning the induced infinitesimal Kobayashi metric, the induced Siegel metric, the L2 Bergman metric, the Teichmüller metric and the Weil–Petersson metric on the Teichmüller space of a compact Riemann surface of genus g⩾2. As a consequence, among others, we show that the moduli space has finite volume with respect to the L2 Bergman metric. This answers a question raised by Nag in 1989.