We derive the shape equations for axisymmetric vesicles and show that they are identical to the general shape equation [Ou-Yang Zhong-Can and W. Helfrich, Phys. Rev. A 39, 5280 (1989)] specialized to axisymmetry. We consider three different topologies (an axisymmetric membrane segment suspended between two circular rings and closed vesicles of spherical and toroidal topology.) We point out that the shape equations are independent of the variational method used.
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Jülicher et al. (1994) studied this question.
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