Abstract
We consider a CanhamHelfrichtype 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 CanhamHelfrich 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 (R. Choksi and M. Veneroni, Calc. Var. Partial Differ. Equ. (2012). DOI:10.1007/s00526-012-0553-9) and prove existence of a global minimizer. Mathematics Subject Classification. 49Q10, 49J45 (58E99, 53C80, 92C10).
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