  We study the Liouville action for quasi-Fuchsian groups with parabolic and
elliptic elements. In particular, when the group is Fuchsian, the contribution
of elliptic elements to the classical Liouville action is derived in terms of
the Bloch-Wigner functions. We prove the first and second variation formulas
for the classical Liouville action on the quasi-Fuchsian deformation space. We
prove an equality expressing the holography principle, which relates the
Liouville action and the renormalized volume for quasi-Fuchsian groups with
parabolic and elliptic elements. We also construct the potential functions of
the K\"ahler forms corresponding to the Takhtajan-Zograf metrics associated to
the elliptic elements in the quasi-Fuchsian groups.
