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Global minimizers for axisymmetric multiphase membranes

Rustum Choksi, Marco Morandotti, Marco Veneroni (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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...

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