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 non-critical 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 reproduces the standard gravitational dressing in the next order of perturbation theory. With the same technique we calculate the intrinsic Hausdorff dimension of a world sheet. 
S. Braune, HU Berlin