  A general framework for the Weyl invariant quantization of Liouville field
theory by means of an exact renormalization group equation is proposed. This
flow equation describes the scale dependence of the effective average action
which has a built-in infrared cutoff. For c<1 it is solved approximately by a
truncation of the space of action functionals. We derive the Ward identities
associated to Weyl transformations in presence of the infrared cutoff. They are
used to select a specific universality class for the renormalization group
trajectory which is found to connect two conformal field theories with central
charges 25-c and 26-c, respectively.
