Nonuniversality in crumpled manifolds

The continuum theory of self-avoiding D-dimensional manifolds with fixed connectivity, in d dimensions, is considered. The exponent {γ} is argued to exist only for integer D It is shown that its {ε}=4D-(2-D)d expansion is not universal at 0({ε}), but depends on the shape of the manifold's boundary. {γ} is calculated for a hyperellipsoid. New universal contact exponents are given for various points of a crumpled manifold.