  It was recently shown that other functionals contribute to the effective
action for the Liouville field when considering massive matter coupled to
two-dimensional gravity in the conformal gauge. The most important of these new
contributions corresponds to the Mabuchi functional. We propose a
minisuperspace action that reproduces the main features of the Mabuchi action
in order to describe the dynamics of the zero-mode. We show that the associated
Hamiltonian coincides with the (quantum mechanical) Liouville Hamiltonian. As a
consequence the Liouville theory and our model of the Mabuchi theory both share
the same spectrum, eigenfunctions and - in this approximation - correlation
functions.
