  We consider a Canham-Helfrich-type variational problem defined over closed
surfaces enclosing a fixed volume and having fixed surface area. The problem
models the shape of multiphase biomembranes. It consists of minimizing the sum
of the Canham-Helfrich energy, in which the bending rigidities and spontaneous
curvatures are now phase-dependent, and a line tension penalization for the
phase interfaces. By restricting attention to axisymmetric surfaces and phase
distributions, we extend our previous results for a single phase
(arXiv:1202.1979) and prove existence of a global minimizer.
