  We study the gravitational action induced by coupling two-dimensional
non-conformal, massive matter to gravity on a compact Riemann surface. We
express this gravitational action in terms of finite and well-defined
quantities for any value of the mass. A small-mass expansion gives back the
Liouville action in the massless limit, the Mabuchi and Aubin-Yau actions to
first order, as well as an infinite series of higher-order contributions
written in terms of purely geometric quantities.
