Stress condensation in crushed elastic manifolds

We discuss an M-dimensional phantom elastic manifold of linear size L crushed into a small sphere of radius R much less than L in N-dimensional space. We investigate the low elastic energy states of 2-sheets (M = 2) and a-sheets (M = 3) using analytic methods and lattice simulations. When N greater than or equal to 2M the curvature energy is uniformly distributed in the sheet and the strain energy is negligible. But when N = M + 1 and M > 1, both energies appear to be condensed into a network of narrow M - 1 dimensional ridges. The ridges appear straight over distances comparable to the confining radius R.