Geodesic
Global minimizers for axisymmetric multiphase membranes
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1014-1029

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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 [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.

DOI : 10.1051/cocv/2012042
Classification : 49Q10, 49J45, 58E99, 53C80, 92C10
Keywords: helfrich functional, biomembranes, global minimizers, axisymmetric surfaces, multicomponent vesicle 
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     author = {Choksi, Rustum and Morandotti, Marco and Veneroni, Marco},
     title = {Global minimizers for axisymmetric multiphase membranes},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1014--1029},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {4},
     year = {2013},
     doi = {10.1051/cocv/2012042},
     mrnumber = {3182678},
     zbl = {1283.49048},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012042/}
}
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Choksi, Rustum; Morandotti, Marco; Veneroni, Marco. Global minimizers for axisymmetric multiphase membranes. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1014-1029. doi: 10.1051/cocv/2012042

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