  Consider a surface, enclosing a fixed volume, described by a free-energy
depending only on the local geometry; for example, the Canham-Helfrich energy
quadratic in the mean curvature describes a fluid membrane. The stress at any
point on the surface is determined completely by geometry. In equilibrium, its
divergence is proportional to the Laplace pressure, normal to the surface,
maintaining the constraint on the volume. It is shown that this source itself
can be expressed as the divergence of a position-dependent surface stress. As a
consequence, the equilibrium can be described in terms of a conserved
`effective' surface stress. Various non-trivial geometrical consequences of
this identification are explored. In a cylindrical geometry, the cross-section
can be viewed as a closed planar Euler elastic curve. With respect to an
appropriate centre the effective stress itself vanishes; this provides a
remarkably simple relationship between the curvature and the position along the
loop. In two or higher dimensions, it is shown that the only geometry
consistent with the vanishing of the effective stress is spherical. It is
argued that the appropriate generalization of the loop result will involve
`null' stresses.
