  I consider the shape of a deformed elastic shell. Using the fact that the
lowest-energy, small deformations are along infinitesimal isometries of the
shell's mid-surface, I describe a class of weakly-stretching deformations for
thin shells based on the Nambu-Goldstone modes associated with those
isometries. The main result is an effective theory to describe the diffuse
deformations of thin shells that incorporate stretching and bending energies.
The theory recovers previous results for the propagation of a "pinch" on a
cylinder. A cone, on the other hand, has two length scales governing the
persistence of a pinch: one governing the relaxation of the pinch that scales
with thickness as a -1/2 power, and one that scales with thickness above which
deformations again become isometric. These lengths meet at a critical thickness
below which low energy deformations again become nearly isometric.
