  It is shown that for monolayer graphene electrons are confined on a perfect
two dimensional surface. The implications for the electronic properties of
corrugated graphene are discussed in view of a derivation of the constrained
relativistic dynamics for the massless carriers in two dimensions. Surface
curvature is related to a series of phenomena with practical applications such
as curvature induced p-n junctions, band gap opening and decoherence. We also
establish a bending free energy by treating graphene as a soft electronic
membrane.
