Intrinsic and extrinsic geometry of random surfaces
Thórdur Jónsson · 1991
Abstract. We prove that the extrinsic Hausdorff dimension is always greater than or equal to the intrinsic Hausdorff dimension in models of triangulated random surfaces with action which is quadratic in the separation of vertices. We furthermore derive a few naive scaling relations which relate the intrinsic Hausdorff dimension to other critical exponents. These relations suggest that the intrinsic Hausdorff The geometrical properties of random surfaces can be studied from two points of view. One can look at the surfaces in an ambient imbedding space as an outside observer or one can study the surfaces as an observer living in the two-dimensional world defined by the surface. The first point of view, the extrinsic one, is appropriate