Anchor ring-vesicle membranes

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Abstract
A family of the exact and analytical solutions of the equilibrium shape equation of vesicle membranes is found. They are anchor rings with generating circles of radii in the ratio 1/ √2 . It is shown that these ring vesicles are stable for some negative values of their spontaneous curvatures, such that experimental construction of such vesicles seems possible. A discussion shows that a positive Gauss-curvature elastic modulus favors the formation of these special vesicles.