We consider the energy of a (2+1)-d relativistic QFT on a deformation of flat space in either the quantum or thermal vacuum state. Looking at both free scalars and fermions, with and without mass (and in the scalar case including a curvature coupling) we surprisingly find that any deformation of flat space is always energetically preferred to flat space itself. This is a UV finite effect, insensitive to any cut- off. We see the same behaviour for any (2+1)-holographic CFT which we compute via the gravity dual. We consider the physical application of this to membranes carrying relativistic degrees of freedom, the vacuum energy of which then induce a tendency for the membrane to crumple. An interesting case is monolayer graphene, which experimentally is observed to ripple, and on large scales can be understood as a membrane carrying free massless Dirac degrees of freedom.