Remarks on invariant metrics on Teichmüller space

We make some comparisons concerning the induced infinitesimal Kobayashi metric, the induced Siegel metric, the L 2 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 L 2 Bergman metric. This answers a question raised by Nag in 1989.