  It was shown recently that, beside the traditional Liouville action, other
functionals appear in the gravitational action of two-dimensional quantum
gravity in the conformal gauge, the most important one being the Mabuchi
functional. In a letter we proposed a minisuperspace action for this theory and
used it to perform its canonical quantization. We found that the Hamiltonian of
the Mabuchi theory is equal to the one of the Liouville theory and thus that
the spectrum and correlation functions match in this approximation. In this
paper we provide motivations to support our conjecture.
