  The variation of energies associated with soft matter interfaces where
surface inhomogeneities are present. These energies include the total bending
and splay energy, the variable surface tension energy, a coupling energy
between the total curvature and an underlying surface concentration field, the
energy due to an external field, and a phase segregation energy. When
considering these energies the variation of material properties such a bending
rigidity are taken into account, which results in more general variation
expressions. These variations can be used to determine the equilibrium
interface and concentration configuration or to determine the driving forces
for non-equilibrium situations. While the focus of this work are energies
associated with multicomponent vesicles, it can easily be extended to any soft
matter interface.
