Instability of Circular Cylinders and Polygonal Solutions for Cylindrical Vesicles

The general solution for cylindrical vesicles is given under the spontaneous curvature model. Detailed analysis shows that shapes without self-intersections are polygonal shapes with n -fold symmetry ( n ≥2). Instability analysis of circular cylinder shows that just as the circular cylinder becomes unstable with respect to the n -mode deformation, polygonal solution with n -fold symmetry begins to appear. Our solution are coincident with the previous numerical calculations. Our results is also valid for various boundary value problems.