Axisymmetric membrane deformation
= Axisymmetric membrane deformation
{title2=$R=R(z)$}
An axisymmetric cylindrical membrane deformation is invariant under rotations about the cylinder axis, so its radius depends only on the axial coordinate. Its <surface area> is $2\pi\int R\sqrt{1+R_z^2}\,dz$, and its enclosed volume is $\pi\int R^2\,dz$. These scalar shape constraints are the basis of the <fixed-volume capillary spectrum of a cylindrical membrane>.