Abstract
We study the fluctuations of membranes with area and curvature elasticity and calculate the renormalization of the curvature elastic constants due to thermal fluctuations. For the mean curvature elastic constant the result is the same as obtained previously for “ideal membranes” which resist only to curvature deformations. The renormalization of the gaussian curvature, on the other hand, depends on the elastic contants. In an incompressible membrane, it is five times weaker than in an ideal membrane.
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