  Unravelling the physical mechanisms behind the organisation of lipid domains
is a central goal in cell biology and membrane biophysics. Previous studies on
cells and model lipid bilayers featuring phase-separated domains found an
intricate interplay between the membrane geometry and its chemical composition.
However, the lack of a model system with simultaneous control over the membrane
shape and conservation of its composition precluded a fundamental understanding
of curvature-induced effects. Here, we present a new class of multicomponent
vesicles supported by colloidal scaffolds of designed shape. We find that the
domain composition adapts to the geometry, giving rise to a novel "antimixed"
state. Theoretical modelling allowed us to link the pinning of domains by
regions of high curvature to the material parameters of the membrane. Our
results provide key insights into the phase separation of cellular membranes
and on curved surfaces in general.
