Inserted: 30 apr 2012
Last Updated: 24 apr 2014
We consider a Canham-Helfrich-type variational problem dened over closed surfaces enclosing a xed volume and having xed 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 $$ and prove existence of a global minimizer.
Keywords: Helfrich functional, biomembranes, global minimizers, axisymmetric surfaces, multicomponent vesicle