We consider the problem to _nd the shape of multiphase biomembranes, mod-

eled as closed surfaces enclosing a _xed volume and having _xed surface area.

The surface energy is assumed to be the sum of two terms: the Canham-Helfrich

energy, in which the bending rigidities and spontaneous curvatures depend on

the phase, and a line tension penalization for the phases interface. By restricting

attention to axisymmetric surfaces and phase distributions, we prove existence

of a global minimizer.

This is a joint work with Rustum Choksi (McGill University, Montreal) and

Marco Morandotti (Instituto Superior Tecnico, Lisbona).