  Motivated by the HRRT-formula for holographic entanglement entropy, we
consider the following question: what are the position and the surface area of
extremal surfaces in a perturbed geometry, given their anchor on the asymptotic
boundary? We derive explicit expressions for the change in position and surface
area, thereby providing a closed form expression for the canonical energy. We
find that a perturbation governed by some small parameter $\lambda$ yields an
expansion of the surface area in terms of a highly non-local expression
involving multiple integrals of geometric quantities over the original extremal
surface.
