  We study the stability and shapes of domains with spontaneous curvature in
fluid films and membranes, embedded in a surrounding membrane with zero
spontaneous curvature. These domains can result from the inclusion of an
impurity in a fluid membrane, or from phase separation within the membrane. We
show that for small but finite line and surface tensions and for finite
spontaneous curvatures, an equilibrium phase of protruding circular domains is
obtained at low impurity concentrations. At higher concentrations, we predict a
transition from circular domains, or "caplets", to stripes. In both cases, we
calculate the shapes of these domains within the Monge representation for the
membrane shape. With increasing line tension, we show numerically that there is
a budding transformation from stable protruding circular domains to spherical
buds. We calculate the full phase diagram, and demonstrate a two triple points,
of respectively bud-flat-caplet and flat-stripe-caplet coexistence.
