Stability of lipid membranes

Lipid membranes are versatile biological structures that undergo significant structural remodelling, often triggered by instabilities. Since they invariably possess heterogeneous properties, owing to the presence of multiple lipid species and their interactions with proteins, heterogeneity can have a significant impact on their equilibrium state and stability. In this work, we use curvature elasticity to derive the generalized stability criterion for heterogeneous lipid membranes. Our formulation entertains strain energies that go beyond the Helfrich energy and exhibit higher-order dependence on curvature invariants or spatially varying properties.