Appears in collection : Conférence à la mémoire de Vadim Knizhnik

We continue the study of $(q, p)$ Minimal Liouville Gravity with the help of Douglas string equation. Generalizing the earlier results we demonstrate that there exist such coordinates τm,n on the space of the perturbed Minimal Liouville Gravity theories, in which the partition function of the theory is determined by the Douglas string equation. The coordinates τm,n are related in a non-linear fashion to the natural coupling constants $\lambda_{m,n}$ of the perturbations of Minimal Liouville Gravity by the physical operators $O_{m,n}$. We find this relation from the requirement that the correlation numbers in Minimal Liouville Gravity must satisfy the conformal and fusion selection rules. After fixing this relation we compute three- and four-point correlation numbers when they are not zero. The results are in agreement with direct calculations in Minimal Liouville Gravity available in the literature.