The statistical mechanics of flexible surfaces with internal elasticity and
shape fluctuations is summarized. Phantom and self-avoiding isotropic and
anisotropic membranes are discussed, with emphasis on the universal negative
Poisson ratio common to the low-temperature phase of phantom membranes and all
strictly self-avoiding membranes in the absence of attractive interactions. The
study of crystalline order on the frozen surface of spherical membranes is also
treated.Comment: Chapter 11 in "Statistical mechanics of Membranes and Surfaces", ed.
by D.R. Nelson, T. Piran and S. Weinberg (World Scientific, Singapore, 2004);
25 pages with 26 figures (high resolution figures available from author
