Global minimizers for axisymmetric multiphase membranes

TL;DR

This paper studies the shape optimization of axisymmetric multiphase biomembranes by minimizing a phase-dependent Canham-Helfrich energy combined with line tension, proving the existence of global minimizers.

Contribution

It extends previous work to multiphase membranes with phase-dependent energies and establishes the existence of global minimizers in the axisymmetric setting.

Findings

Existence of global minimizers for the multiphase membrane problem.

Extension of previous single-phase results to multiphase cases.

Framework for analyzing phase-dependent membrane shapes.

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.