The equivalence of two approaches to the variational theory of cell-membrane equilibria which have been proposed in the literature is demonstrated. Both assume a constraint on surface area, global in one formulation and local in the alternative, in accordance with measurements which reveal negligible surface dilation in the presence of membrane deformation. We thus address a potential controversy in the mathematical modeling of an important problem in biophysics.
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David Steigmann, Eveline Baesu, Robert E. Rudd, Jim Belak, Mike McElfresh, On the variational theory of cell-membrane equilibria. Interfaces Free Bound. 5 (2003), no. 4, pp. 357–366DOI 10.4171/IFB/83