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

Nambu-Goldstone modes and diffuse deformations in elastic shells