  Regularity of the deformation of the Fermi surface under short-range
interactions is established to all orders in perturbation theory. The proofs
are based on a new classification of all graphs that are not doubly
overlapping. They turn out to be generalized RPA graphs. This provides a simple
extension to all orders of the regularity theorem of the Fermi surface movement
proven in [FST2]. Models in which the Fermi surface is not symmetric under the
reflection p to -p are included.
