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Phase separation within the fluid membrane of a vesicle can lead to domain-induced budding. This shape transformation should occur both for the spinodal decomposition and for the nucleation regime and should be observable in quench experiments on phospholipid-cholesterol vesicles. The budding process leads to limit shapes for which the bud is connected by an infinitesimal neck to the original vesicle. This neck can be characterized by a general relation for the principal curvatures of the adjacent membrane segments. The effect of the Gaussian curvature on the shape is also discussed.