Abstract: We study the confinement of Dirac fermions in graphene and in
carbon nanotubes by an external magnetic field, mechanical deformations or
inhomogeneities in the substrate. By applying variational principles to the
square of the Dirac operator, we obtain sufficient and necessary conditions
for confinement of the quasi-particles. The rigorous theoretical results are
illustrated on the realistic examples of the three classes of traps.