SHAPE EQUATION AND SHAPES OF AXISYMMETRIC VESICLES IN TOROIDAL TOPOLOGY

For toroidal topology we solve the shape equation for axisymmetric vesicles numerically. The phase diagram is found to be similar to that from another shape equation. This similarity is the result of the insensitive dependence of beading energy upon detailed shape of vesicles and the constant volume and area ensemble we are considering. We argue that the very small distance between two opposite cusps of the sickle-shaped vesicle makes it unstable and fuse into two encompassed spheres which might be observed in experiment. The spontaneous curvatures of the observed Clifford tori are also estimated.