Global minimizers for axisymmetric multiphase membranes

2012/04/30 by Rustum Choksi, Marco Morandotti, Choksi, Rustum +3
Medicine · Biochemistry, Genetics and Molecular Biology · Immunology and Microbiology · #Cell Adhesion Molecules Research #Cellular Mechanics and Interactions #Phagocytosis and Immune Regulation

paper · pdf · doi:10.48550/arxiv.1204.6673

Abstract

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 (arXiv:1202.1979) and prove existence of a global minimizer.

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