Deformations of the geometry of lipid vesicles

TL;DR

This paper investigates the stability of lipid vesicle shapes by analyzing the second variation of a curvature-dependent Hamiltonian using a surface covariant approach, identifying the operator governing equilibrium stability.

Contribution

It introduces a surface covariant method to compute the second variation of the curvature-based Hamiltonian for lipid vesicles, advancing understanding of their stability analysis.

Findings

Derived the operator governing stability of vesicle equilibria

Provided a covariant framework for second variation analysis

Enhanced understanding of vesicle shape stability

Abstract

Consider a closed lipid membrane (vesicle), modeled as a two-dimensional surface, described by a geometrical hamiltonian that depends on its extrinsic curvature. The vanishing of its first variation determines the equilibrium configurations for the system. In this paper, we examine the second variation of the hamiltonian about any given equilibrium, using an explicitly surface covariant geometrical approach. We identify the operator which determines the stability of equilibrium configurations.