Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effect of Thermal Undulations on the Bending Elasticity and Spontaneous
  Curvature of Fluid Membranes   We amplify previous arguments why mean curvature should be used as measure of
integration in calculating the effective bending rigidity of fluid membranes
subjected to a weak background curvature. The stiffening of the membrane by its
fluctuations, recently derived for spherical shapes, is recovered for
cylindrical curvature. Employing curvilinear coordinates, we then discuss
stiffening for arbitrary shapes, confirm that the elastic modulus of Gaussian
curvature is not renormalized in the presence of fluctuations, and show for the
first time that any spontaneous curvature also remains unchanged.

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The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an