Abstract
Vesicles are closed surfaces of bilayer membranes. Their mean shapes and fluctuations are governed by the competition of curvature energy and geometrical constraints on the enclosed volume and total surface area. A scheme to calculate these fluctuations to lowest order in the ratio of temperature to bending rigidity is developed. It is shown that for fluctuations that break a symmetry of the mean shape the area constraint indeed acts like a tension whose value is given by the Lagrange multiplier used to enforce the area constraint in the first place. As a consequence, these fluctuations are also insensitive to the specific variants of the curvature model. For fluctuations that preserve the symmetry of the mean shape the role of the area constraint is more subtle. The low temperature expansion breaks down in the spherical limit where with the excess area another small parameter enters. By incorporating the area constraint in this limit exactly, the validity of the conventional approach using an effective tension for fluctuations of quasi-spherical vesicles can be assessed.
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Dedicated to Prof. Herbert Wagner on the occasion of his 60th birthday