F. Julicher et U. Seifert, SHAPE EQUATIONS FOR AXISYMMETRICAL VESICLES - A CLARIFICATION, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(5), 1994, pp. 4728-4731
We derive the shape equations for axisymmetric vesicles and show that
they are identical to the general shape equation [Ou-Yang Zhong-Can an
d W. Helfrich, Phys. Rev. A 39, 5280 (1989)] specialized to axisymmetr
y. We consider three different topologies (an axisymmetric membrane se
gment suspended between two circular rings and closed vesicles of sphe
rical and toroidal topology). We point out that the shape equations ar
e independent of the variational method used.