Geometrical properties of conformal field theories coupled to two-dimensional quantum gravity

In this work we discuss an approach due to F. David to the geometry of world sheets of noncritical strings in quasiclassical approximation. The gravitational dressed conformal dimension is related to the scaling behavior of the two-point function with respect to a distance-variable. We show how this approach can reproduce the standard gravitational dressing in the next order of perturbation theory. Furthermore, we try to find this scaling dimension by studying the functional integral. With the same technique we calculate the intrinsic Hausdorff dimension of a world sheet.