Helfrich cylinders -- instabilities, bifurcations and amplitude equations

Combining local bifurcation analysis with numerical continuation and bifurcation methods we study bifurcations from cylindrical vesicles described by the Helfrich equation with volume and area constraints, with a prescribed periodicity along the cylindrical axis. The bifurcating solutions are in two main classes, axisymmetric (pearling), and non-axisymmetric (coiling, buckling, and wrinkling), and depending on the spontaneous curvature and the prescribed periodicity along the cylinder axis we obtain different stabilities of the bifurcating branches, and different secondary bifurcations.