Conformation fluctuations of polymerized vesicles in the inextensible and flexible limit

We study conformation fluctuations of a tethered membrane of spherical shape. The membrane is assumed to be both inextensible and flexible. We first study Linear fluctuations and show that they are irrelevant in this limit. Nonlinear fluctuations can be described in terms of isometric buckling of local circular portions of the membrane. Configurations of buckled regions on the membrane are then modeled as a system of rings whose excitation energies are the elastic energy cost of buckling. The rings should be nonoverlapping with one another due to geometrical constraints. We study the the thermodynamics of this system using a variational method, and the results are interpreted in terms of the shape fluctuations of the membrane itself. Our results indicate that there is no roughening transition when we raise the temperature. In other words, the membrane remains ''flat'' at all temperatures even though it is made of very flexible material.