  We compare the standard and geometric approaches to quantum Liouville theory
on the pseudosphere by performing perturbative calculations of the one and two
point functions up to the third order in the coupling constant. The choice of
the Hadamard regularization within the geometric approach leads to a
discrepancy with the standard approach. On the other hand, we find complete
agreement between the results of the standard approach and the bootstrap
conjectures for the one point function and the auxiliary two point function.
