We show that a strong segregation of a two-component surfactant system coupled to the local membrane curvature has a pronounced effect on the shape of unilamellae or closed vesicles. For an average flat lamella, the preferred periodicity in the local composition as well as the lamellar shape is calculated and depends on the ratio between surface tension and bending modulus. In the case of a closed visicle with a fixed total area, there is no selected periodicity in contrast to the unilamellar case. For vesicles subjected to positive or negative inner pressure, we calculate their shape numerically, whereas when there is no added inner pressure, the shape is found analytically to be composed of circular sections.
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