We consider equilibria of models for Giant Unilamellar Vesicles (GUVs), which are closed lipid-bilayer membranes of radii on the order of microns. Recent breakthroughs in imaging reveal highly complex equilibrium shapes of nominally spherical vesicles (with "broken" spherical symmetry)under excess external pressure [1]. We consider both a classical single-phase model [2] and propose a two-phase model (in mean curvature) with higher-gradient regularization. For the former we demonstrate that the "first" instability is always axisymmetric, while the latter reveals the possiblity of complex higher-mode bifurcations, which we analyze via well known group-theoretic techniques [3].
[1] T. Baumgart, et. al., Nature, Vol 425 (2003)821-824. [2] J. T. Jenkins, J. Math. Biol., Vol. 4 (1976) 149-169. [3] M. Golubitsky, et. al., Symmetry and Groups in Bifurcation Theory II, Springer (1988).
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