Soliton Surfaces in the Mechanical Equilibrium of Closed Membranes

  title={Soliton Surfaces in the Mechanical Equilibrium of Closed Membranes},
  author={Brian P. Smyth},
  journal={Communications in Mathematical Physics},
  • Brian P. Smyth
  • Published 2004
  • Mathematics
  • Communications in Mathematical Physics
  • For a closed material membrane in equilibrium in a force field we investigate whether the external observables (membrane geometry and force field) determine the internal membrane response (the stress tensor T), when the mean stress Tr T is known. For membranes with boundary the indeterminacy of the response is classical. For closed membranes the geometry decides the question. We show uniqueness for all but a class of soliton surfaces — the globally isothermic surfaces (§1, 2); the physical… CONTINUE READING


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