WORLD-SHEET GEOMETRY AND BABY UNIVERSES IN 2D QUANTUM-GRAVITY

We show that the surface roughness for c < 1 matter theories coupled to 2D quantum gravity is described by a self-similar structure of baby universes. There exist baby universes whose neck thickness is of the order of the ultraviolet cutoff, the largest of these having a macroscopic area approximately A1/(1 - gamma), where A is the total area and gamma the string susceptibility exponent.